3w^2=15w

{ "query": { "display": "$$3w^{2}=15w$$", "symbolab_question": "EQUATION#3w^{2}=15w" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Quadratic", "default": "w=0,w=5", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$3w^{2}=15w{\\quad:\\quad}w=0,\\:w=5$$", "input": "3w^{2}=15w", "steps": [ { "type": "interim", "title": "Move $$15w\\:$$to the left side", "input": "3w^{2}=15w", "result": "3w^{2}-15w=0", "steps": [ { "type": "step", "primary": "Subtract $$15w$$ from both sides", "result": "3w^{2}-15w=15w-15w" }, { "type": "step", "primary": "Simplify", "result": "3w^{2}-15w=0" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Factor $$3w^{2}-15w:{\\quad}3w\\left(w-5\\right)$$", "input": "3w^{2}-15w", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{b+c}=a^{b}a^{c}$$", "secondary": [ "$$w^{2}=ww$$" ], "result": "=3ww-15w", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Rewrite $$15$$ as $$3\\cdot\\:5$$", "result": "=3ww-3\\cdot\\:5w" }, { "type": "step", "primary": "Factor out common term $$3w$$", "result": "=3w\\left(w-5\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "3w\\left(w-5\\right)=0" }, { "type": "step", "primary": "Using the Zero Factor Principle:$$\\quad$$ If $$ab=0\\:$$then $$a=0\\:$$or $$b=0$$", "result": "w=0\\lor\\:w-5=0" }, { "type": "interim", "title": "Solve $$w-5=0:{\\quad}w=5$$", "input": "w-5=0", "steps": [ { "type": "interim", "title": "Move $$5\\:$$to the right side", "input": "w-5=0", "result": "w=5", "steps": [ { "type": "step", "primary": "Add $$5$$ to both sides", "result": "w-5+5=0+5" }, { "type": "step", "primary": "Simplify", "result": "w=5" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "primary": "The solutions to the quadratic equation are:", "result": "w=0,\\:w=5" } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/quadratic-equations-practice", "practiceTopic": "Quadratic Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "w", "plotRequest": "3w^{2}-15w" }, "showViewLarger": true } }, "meta": { "showVerify": true } }