(2x-13)(12x+7)=-91

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Solution for (2x-13)(12x+7)=-91 equation: 


Simplifying
(2x + -13)(12x + 7) = -91

Reorder the terms:
(-13 + 2x)(12x + 7) = -91

Reorder the terms:
(-13 + 2x)(7 + 12x) = -91

Multiply (-13 + 2x) * (7 + 12x)
(-13(7 + 12x) + 2x * (7 + 12x)) = -91
((7 * -13 + 12x * -13) + 2x * (7 + 12x)) = -91
((-91 + -156x) + 2x * (7 + 12x)) = -91
(-91 + -156x + (7 * 2x + 12x * 2x)) = -91
(-91 + -156x + (14x + 24x2)) = -91

Combine like terms: -156x + 14x = -142x
(-91 + -142x + 24x2) = -91

Add '91' to each side of the equation.
-91 + -142x + 91 + 24x2 = -91 + 91

Reorder the terms:
-91 + 91 + -142x + 24x2 = -91 + 91

Combine like terms: -91 + 91 = 0
0 + -142x + 24x2 = -91 + 91
-142x + 24x2 = -91 + 91

Combine like terms: -91 + 91 = 0
-142x + 24x2 = 0

Solving
-142x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-71 + 12x) = 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 '(-71 + 12x)' equal to zero and attempt to solve:

Simplifying
-71 + 12x = 0

Solving
-71 + 12x = 0

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

Add '71' to each side of the equation.
-71 + 71 + 12x = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 12x = 0 + 71
12x = 0 + 71

Combine like terms: 0 + 71 = 71
12x = 71

Divide each side by '12'.
x = 5.916666667

Simplifying
x = 5.916666667
Solution
x = {0, 5.916666667}

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