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

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


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

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

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

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

Combine like terms: 10x + -10x = 0
(-25 + 0 + 4x2) + 25 = 2x
(-25 + 4x2) + 25 = 2x

Reorder the terms:
-25 + 25 + 4x2 = 2x

Combine like terms: -25 + 25 = 0
0 + 4x2 = 2x
4x2 = 2x

Solving
4x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-2x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + 2x) = 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}

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