(2x+5)(2x-5)=4x-25

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Solution for (2x+5)(2x-5)=4x-25 equation: 


Simplifying
(2x + 5)(2x + -5) = 4x + -25

Reorder the terms:
(5 + 2x)(2x + -5) = 4x + -25

Reorder the terms:
(5 + 2x)(-5 + 2x) = 4x + -25

Multiply (5 + 2x) * (-5 + 2x)
(5(-5 + 2x) + 2x * (-5 + 2x)) = 4x + -25
((-5 * 5 + 2x * 5) + 2x * (-5 + 2x)) = 4x + -25
((-25 + 10x) + 2x * (-5 + 2x)) = 4x + -25
(-25 + 10x + (-5 * 2x + 2x * 2x)) = 4x + -25
(-25 + 10x + (-10x + 4x2)) = 4x + -25

Combine like terms: 10x + -10x = 0
(-25 + 0 + 4x2) = 4x + -25
(-25 + 4x2) = 4x + -25

Reorder the terms:
-25 + 4x2 = -25 + 4x

Add '25' to each side of the equation.
-25 + 25 + 4x2 = -25 + 25 + 4x

Combine like terms: -25 + 25 = 0
0 + 4x2 = -25 + 25 + 4x
4x2 = -25 + 25 + 4x

Combine like terms: -25 + 25 = 0
4x2 = 0 + 4x
4x2 = 4x

Solving
4x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-4x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1 + x) = 0

Ignore the factor 4.

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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}

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