(6x-9)x(6x+9)=

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Solution for (6x-9)x(6x+9)= equation: 


Simplifying
(6x + -9) * x(6x + 9) = 0

Reorder the terms:
(-9 + 6x) * x(6x + 9) = 0

Reorder the terms:
(-9 + 6x) * x(9 + 6x) = 0

Reorder the terms for easier multiplication:
x(-9 + 6x)(9 + 6x) = 0

Multiply (-9 + 6x) * (9 + 6x)
x(-9(9 + 6x) + 6x * (9 + 6x)) = 0
x((9 * -9 + 6x * -9) + 6x * (9 + 6x)) = 0
x((-81 + -54x) + 6x * (9 + 6x)) = 0
x(-81 + -54x + (9 * 6x + 6x * 6x)) = 0
x(-81 + -54x + (54x + 36x2)) = 0

Combine like terms: -54x + 54x = 0
x(-81 + 0 + 36x2) = 0
x(-81 + 36x2) = 0
(-81 * x + 36x2 * x) = 0
(-81x + 36x3) = 0

Solving
-81x + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-9 + 4x2) = 0

Factor a difference between two squares.
9x((3 + 2x)(-3 + 2x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 3
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -1.5, 1.5}

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