(3x^2+4x)(3x^2-4x)=

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Solution for (3x^2+4x)(3x^2-4x)= equation: 


Simplifying
(3x2 + 4x)(3x2 + -4x) = 0

Reorder the terms:
(4x + 3x2)(3x2 + -4x) = 0

Reorder the terms:
(4x + 3x2)(-4x + 3x2) = 0

Multiply (4x + 3x2) * (-4x + 3x2)
(4x * (-4x + 3x2) + 3x2 * (-4x + 3x2)) = 0
((-4x * 4x + 3x2 * 4x) + 3x2 * (-4x + 3x2)) = 0
((-16x2 + 12x3) + 3x2 * (-4x + 3x2)) = 0
(-16x2 + 12x3 + (-4x * 3x2 + 3x2 * 3x2)) = 0
(-16x2 + 12x3 + (-12x3 + 9x4)) = 0

Combine like terms: 12x3 + -12x3 = 0
(-16x2 + 0 + 9x4) = 0
(-16x2 + 9x4) = 0

Solving
-16x2 + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-16 + 9x2) = 0

Factor a difference between two squares.
x2((4 + 3x)(-4 + 3x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 3
Set the factor '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -1.333333333, 1.333333333}

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