What are the solutions to the equation solvefor A,A^3=A^2B-3A^2 ?

The solutions to the equation solvefor A,A^3=A^2B-3A^2 are A=0,A=B-3

Find the zeros of solvefor A,A^3=A^2B-3A^2

The zeros of solvefor A,A^3=A^2B-3A^2 are A=0,A=B-3

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solve for

A, A^{3} = A^{2} B - 3 A^{2}

A = 0, A = B - 3

Solution steps

A^{3} = A^{2} B - 3 A^{2}

Subtract

A^{2} B - 3 A^{2}

from both sides

A^{3} - (A^{2} B - 3 A^{2}) = A^{2} B - 3 A^{2} - (A^{2} B - 3 A^{2})

Simplify

A^{3} - A^{2} B + 3 A^{2} = 0

Factor

A^{3} - A^{2} B + 3 A^{2} : A^{2} (A - B + 3)

A^{2} (A - B + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

A = 0 or A - B + 3 = 0

Solve

A - B + 3 = 0 : A = B - 3

The solutions are

A = 0, A = B - 3

w^{3} = - 2 - 2 i 3

(x^{2} - x)^{2} - (x^{2} - x) - 12 = 0

x, y = x^{5}

x^{3} - 7 x^{2} + 5 x + 6 = 0

3 y^{4} - 5 y^{3} + 2 y^{2} = 0

What are the solutions to the equation solvefor A,A^3=A^2B-3A^2 ?
The solutions to the equation solvefor A,A^3=A^2B-3A^2 are A=0,A=B-3
Find the zeros of solvefor A,A^3=A^2B-3A^2
The zeros of solvefor A,A^3=A^2B-3A^2 are A=0,A=B-3