(2x-8)(x+7)=11x+7

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Solution for (2x-8)(x+7)=11x+7 equation: 


Simplifying
(2x + -8)(x + 7) = 11x + 7

Reorder the terms:
(-8 + 2x)(x + 7) = 11x + 7

Reorder the terms:
(-8 + 2x)(7 + x) = 11x + 7

Multiply (-8 + 2x) * (7 + x)
(-8(7 + x) + 2x * (7 + x)) = 11x + 7
((7 * -8 + x * -8) + 2x * (7 + x)) = 11x + 7
((-56 + -8x) + 2x * (7 + x)) = 11x + 7
(-56 + -8x + (7 * 2x + x * 2x)) = 11x + 7
(-56 + -8x + (14x + 2x2)) = 11x + 7

Combine like terms: -8x + 14x = 6x
(-56 + 6x + 2x2) = 11x + 7

Reorder the terms:
-56 + 6x + 2x2 = 7 + 11x

Solving
-56 + 6x + 2x2 = 7 + 11x

Solving for variable 'x'.

Reorder the terms:
-56 + -7 + 6x + -11x + 2x2 = 7 + 11x + -7 + -11x

Combine like terms: -56 + -7 = -63
-63 + 6x + -11x + 2x2 = 7 + 11x + -7 + -11x

Combine like terms: 6x + -11x = -5x
-63 + -5x + 2x2 = 7 + 11x + -7 + -11x

Reorder the terms:
-63 + -5x + 2x2 = 7 + -7 + 11x + -11x

Combine like terms: 7 + -7 = 0
-63 + -5x + 2x2 = 0 + 11x + -11x
-63 + -5x + 2x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-63 + -5x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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 = {-4.5, 7}

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