(x+6)(x-2)-(8x-7)=0

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Solution for (x+6)(x-2)-(8x-7)=0 equation: 


Simplifying
(x + 6)(x + -2) + -1(8x + -7) = 0

Reorder the terms:
(6 + x)(x + -2) + -1(8x + -7) = 0

Reorder the terms:
(6 + x)(-2 + x) + -1(8x + -7) = 0

Multiply (6 + x) * (-2 + x)
(6(-2 + x) + x(-2 + x)) + -1(8x + -7) = 0
((-2 * 6 + x * 6) + x(-2 + x)) + -1(8x + -7) = 0
((-12 + 6x) + x(-2 + x)) + -1(8x + -7) = 0
(-12 + 6x + (-2 * x + x * x)) + -1(8x + -7) = 0
(-12 + 6x + (-2x + x2)) + -1(8x + -7) = 0

Combine like terms: 6x + -2x = 4x
(-12 + 4x + x2) + -1(8x + -7) = 0

Reorder the terms:
-12 + 4x + x2 + -1(-7 + 8x) = 0
-12 + 4x + x2 + (-7 * -1 + 8x * -1) = 0
-12 + 4x + x2 + (7 + -8x) = 0

Reorder the terms:
-12 + 7 + 4x + -8x + x2 = 0

Combine like terms: -12 + 7 = -5
-5 + 4x + -8x + x2 = 0

Combine like terms: 4x + -8x = -4x
-5 + -4x + x2 = 0

Solving
-5 + -4x + x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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