(2x+13)(2x-13)=4x-169

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Solution for (2x+13)(2x-13)=4x-169 equation: 


Simplifying
(2x + 13)(2x + -13) = 4x + -169

Reorder the terms:
(13 + 2x)(2x + -13) = 4x + -169

Reorder the terms:
(13 + 2x)(-13 + 2x) = 4x + -169

Multiply (13 + 2x) * (-13 + 2x)
(13(-13 + 2x) + 2x * (-13 + 2x)) = 4x + -169
((-13 * 13 + 2x * 13) + 2x * (-13 + 2x)) = 4x + -169
((-169 + 26x) + 2x * (-13 + 2x)) = 4x + -169
(-169 + 26x + (-13 * 2x + 2x * 2x)) = 4x + -169
(-169 + 26x + (-26x + 4x2)) = 4x + -169

Combine like terms: 26x + -26x = 0
(-169 + 0 + 4x2) = 4x + -169
(-169 + 4x2) = 4x + -169

Reorder the terms:
-169 + 4x2 = -169 + 4x

Add '169' to each side of the equation.
-169 + 169 + 4x2 = -169 + 169 + 4x

Combine like terms: -169 + 169 = 0
0 + 4x2 = -169 + 169 + 4x
4x2 = -169 + 169 + 4x

Combine like terms: -169 + 169 = 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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