What are the solutions to the equation 12x^2-4x^2=x^3 ?

The solutions to the equation 12x^2-4x^2=x^3 are x=0,x=8

Find the zeros of 12x^2-4x^2=x^3

The zeros of 12x^2-4x^2=x^3 are x=0,x=8

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12 x^{2} - 4 x^{2} = x^{3}

x = 0, x = 8

Solution steps

12 x^{2} - 4 x^{2} = x^{3}

Switch sides

x^{3} = 12 x^{2} - 4 x^{2}

Subtract

12 x^{2} - 4 x^{2}

from both sides

x^{3} - (12 x^{2} - 4 x^{2}) = 12 x^{2} - 4 x^{2} - (12 x^{2} - 4 x^{2})

Simplify

x^{3} - 8 x^{2} = 0

Factor

x^{3} - 8 x^{2} : x^{2} (x - 8)

x^{2} (x - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 8 = 0

Solve

x - 8 = 0 : x = 8

The solutions are

x = 0, x = 8

20 y^{4} + 160 y^{2} - 285 = 0

27000 = 20000 \cdot (1 + x)^{6}

84 x^{3} - 71 x^{2} - 117 x - 28 = 0

X^{4} - 3 X^{2} = 0

3 x^{3} + 1 6^{2} = 12 x

What are the solutions to the equation 12x^2-4x^2=x^3 ?
The solutions to the equation 12x^2-4x^2=x^3 are x=0,x=8
Find the zeros of 12x^2-4x^2=x^3
The zeros of 12x^2-4x^2=x^3 are x=0,x=8