(x+8)(x-6)=(2x+1)(x-6)

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Solution for (x+8)(x-6)=(2x+1)(x-6) equation: 


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

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

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

Multiply (8 + x) * (-6 + x)
(8(-6 + x) + x(-6 + x)) = (2x + 1)(x + -6)
((-6 * 8 + x * 8) + x(-6 + x)) = (2x + 1)(x + -6)
((-48 + 8x) + x(-6 + x)) = (2x + 1)(x + -6)
(-48 + 8x + (-6 * x + x * x)) = (2x + 1)(x + -6)
(-48 + 8x + (-6x + x2)) = (2x + 1)(x + -6)

Combine like terms: 8x + -6x = 2x
(-48 + 2x + x2) = (2x + 1)(x + -6)

Reorder the terms:
-48 + 2x + x2 = (1 + 2x)(x + -6)

Reorder the terms:
-48 + 2x + x2 = (1 + 2x)(-6 + x)

Multiply (1 + 2x) * (-6 + x)
-48 + 2x + x2 = (1(-6 + x) + 2x * (-6 + x))
-48 + 2x + x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x))
-48 + 2x + x2 = ((-6 + 1x) + 2x * (-6 + x))
-48 + 2x + x2 = (-6 + 1x + (-6 * 2x + x * 2x))
-48 + 2x + x2 = (-6 + 1x + (-12x + 2x2))

Combine like terms: 1x + -12x = -11x
-48 + 2x + x2 = (-6 + -11x + 2x2)

Solving
-48 + 2x + x2 = -6 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-48 + 6 + 2x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: -48 + 6 = -42
-42 + 2x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: 2x + 11x = 13x
-42 + 13x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-42 + 13x + -1x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Reorder the terms:
-42 + 13x + -1x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
-42 + 13x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2
-42 + 13x + -1x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-42 + 13x + -1x2 = 0 + 2x2 + -2x2
-42 + 13x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-42 + 13x + -1x2 = 0

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


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {7, 6}

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