(2x-13)(2x-7)=91

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Solution for (2x-13)(2x-7)=91 equation: 


Simplifying
(2x + -13)(2x + -7) = 91

Reorder the terms:
(-13 + 2x)(2x + -7) = 91

Reorder the terms:
(-13 + 2x)(-7 + 2x) = 91

Multiply (-13 + 2x) * (-7 + 2x)
(-13(-7 + 2x) + 2x * (-7 + 2x)) = 91
((-7 * -13 + 2x * -13) + 2x * (-7 + 2x)) = 91
((91 + -26x) + 2x * (-7 + 2x)) = 91
(91 + -26x + (-7 * 2x + 2x * 2x)) = 91
(91 + -26x + (-14x + 4x2)) = 91

Combine like terms: -26x + -14x = -40x
(91 + -40x + 4x2) = 91

Add '-91' to each side of the equation.
91 + -40x + -91 + 4x2 = 91 + -91

Reorder the terms:
91 + -91 + -40x + 4x2 = 91 + -91

Combine like terms: 91 + -91 = 0
0 + -40x + 4x2 = 91 + -91
-40x + 4x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-40x + 4x2 = 0

Solving
-40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-10 + 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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, 10}

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