(3x-8)(2x-7)=91

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Solution for (3x-8)(2x-7)=91 equation: 


Simplifying
(3x + -8)(2x + -7) = 91

Reorder the terms:
(-8 + 3x)(2x + -7) = 91

Reorder the terms:
(-8 + 3x)(-7 + 2x) = 91

Multiply (-8 + 3x) * (-7 + 2x)
(-8(-7 + 2x) + 3x * (-7 + 2x)) = 91
((-7 * -8 + 2x * -8) + 3x * (-7 + 2x)) = 91
((56 + -16x) + 3x * (-7 + 2x)) = 91
(56 + -16x + (-7 * 3x + 2x * 3x)) = 91
(56 + -16x + (-21x + 6x2)) = 91

Combine like terms: -16x + -21x = -37x
(56 + -37x + 6x2) = 91

Solving
56 + -37x + 6x2 = 91

Solving for variable 'x'.

Reorder the terms:
56 + -91 + -37x + 6x2 = 91 + -91

Combine like terms: 56 + -91 = -35
-35 + -37x + 6x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-35 + -37x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

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 = {-0.8333333333, 7}

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