(2x-13)(2x-7)-(2x-7)=0

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Solution for (2x-13)(2x-7)-(2x-7)=0 equation: 


Simplifying
(2x + -13)(2x + -7) + -1(2x + -7) = 0

Reorder the terms:
(-13 + 2x)(2x + -7) + -1(2x + -7) = 0

Reorder the terms:
(-13 + 2x)(-7 + 2x) + -1(2x + -7) = 0

Multiply (-13 + 2x) * (-7 + 2x)
(-13(-7 + 2x) + 2x * (-7 + 2x)) + -1(2x + -7) = 0
((-7 * -13 + 2x * -13) + 2x * (-7 + 2x)) + -1(2x + -7) = 0
((91 + -26x) + 2x * (-7 + 2x)) + -1(2x + -7) = 0
(91 + -26x + (-7 * 2x + 2x * 2x)) + -1(2x + -7) = 0
(91 + -26x + (-14x + 4x2)) + -1(2x + -7) = 0

Combine like terms: -26x + -14x = -40x
(91 + -40x + 4x2) + -1(2x + -7) = 0

Reorder the terms:
91 + -40x + 4x2 + -1(-7 + 2x) = 0
91 + -40x + 4x2 + (-7 * -1 + 2x * -1) = 0
91 + -40x + 4x2 + (7 + -2x) = 0

Reorder the terms:
91 + 7 + -40x + -2x + 4x2 = 0

Combine like terms: 91 + 7 = 98
98 + -40x + -2x + 4x2 = 0

Combine like terms: -40x + -2x = -42x
98 + -42x + 4x2 = 0

Solving
98 + -42x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(49 + -21x + 2x2) = 0

Factor a trinomial.
2((7 + -2x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3.5, 7}

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