(x+6)(x-5)=10x-8

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Solution for (x+6)(x-5)=10x-8 equation: 


Simplifying
(x + 6)(x + -5) = 10x + -8

Reorder the terms:
(6 + x)(x + -5) = 10x + -8

Reorder the terms:
(6 + x)(-5 + x) = 10x + -8

Multiply (6 + x) * (-5 + x)
(6(-5 + x) + x(-5 + x)) = 10x + -8
((-5 * 6 + x * 6) + x(-5 + x)) = 10x + -8
((-30 + 6x) + x(-5 + x)) = 10x + -8
(-30 + 6x + (-5 * x + x * x)) = 10x + -8
(-30 + 6x + (-5x + x2)) = 10x + -8

Combine like terms: 6x + -5x = 1x
(-30 + 1x + x2) = 10x + -8

Reorder the terms:
-30 + 1x + x2 = -8 + 10x

Solving
-30 + 1x + x2 = -8 + 10x

Solving for variable 'x'.

Reorder the terms:
-30 + 8 + 1x + -10x + x2 = -8 + 10x + 8 + -10x

Combine like terms: -30 + 8 = -22
-22 + 1x + -10x + x2 = -8 + 10x + 8 + -10x

Combine like terms: 1x + -10x = -9x
-22 + -9x + x2 = -8 + 10x + 8 + -10x

Reorder the terms:
-22 + -9x + x2 = -8 + 8 + 10x + -10x

Combine like terms: -8 + 8 = 0
-22 + -9x + x2 = 0 + 10x + -10x
-22 + -9x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-22 + -9x + x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-2, 11}

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