2x(4x+5)(4x-5)=0

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Solution for 2x(4x+5)(4x-5)=0 equation: 


Simplifying
2x(4x + 5)(4x + -5) = 0

Reorder the terms:
2x(5 + 4x)(4x + -5) = 0

Reorder the terms:
2x(5 + 4x)(-5 + 4x) = 0

Multiply (5 + 4x) * (-5 + 4x)
2x(5(-5 + 4x) + 4x * (-5 + 4x)) = 0
2x((-5 * 5 + 4x * 5) + 4x * (-5 + 4x)) = 0
2x((-25 + 20x) + 4x * (-5 + 4x)) = 0
2x(-25 + 20x + (-5 * 4x + 4x * 4x)) = 0
2x(-25 + 20x + (-20x + 16x2)) = 0

Combine like terms: 20x + -20x = 0
2x(-25 + 0 + 16x2) = 0
2x(-25 + 16x2) = 0
(-25 * 2x + 16x2 * 2x) = 0
(-50x + 32x3) = 0

Solving
-50x + 32x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-25 + 16x2) = 0

Factor a difference between two squares.
2x((5 + 4x)(-5 + 4x)) = 0

Ignore the factor 2.

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 '(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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