(4x^2+5x)(4x^2-5x)=

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Solution for (4x^2+5x)(4x^2-5x)= equation: 


Simplifying
(4x2 + 5x)(4x2 + -5x) = 0

Reorder the terms:
(5x + 4x2)(4x2 + -5x) = 0

Reorder the terms:
(5x + 4x2)(-5x + 4x2) = 0

Multiply (5x + 4x2) * (-5x + 4x2)
(5x * (-5x + 4x2) + 4x2 * (-5x + 4x2)) = 0
((-5x * 5x + 4x2 * 5x) + 4x2 * (-5x + 4x2)) = 0
((-25x2 + 20x3) + 4x2 * (-5x + 4x2)) = 0
(-25x2 + 20x3 + (-5x * 4x2 + 4x2 * 4x2)) = 0
(-25x2 + 20x3 + (-20x3 + 16x4)) = 0

Combine like terms: 20x3 + -20x3 = 0
(-25x2 + 0 + 16x4) = 0
(-25x2 + 16x4) = 0

Solving
-25x2 + 16x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-25 + 16x2) = 0

Factor a difference between two squares.
x2((5 + 4x)(-5 + 4x)) = 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 '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 3
Set the factor '(-5 + 4x)' equal to zero and attempt to solve:

Simplifying
-5 + 4x = 0

Solving
-5 + 4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4x = 0 + 5
4x = 0 + 5

Combine like terms: 0 + 5 = 5
4x = 5

Divide each side by '4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0, -1.25, 1.25}

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