(x+2)(x-6)=(2x+3)(x-6)

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Solution for (x+2)(x-6)=(2x+3)(x-6) equation: 


Simplifying
(x + 2)(x + -6) = (2x + 3)(x + -6)

Reorder the terms:
(2 + x)(x + -6) = (2x + 3)(x + -6)

Reorder the terms:
(2 + x)(-6 + x) = (2x + 3)(x + -6)

Multiply (2 + x) * (-6 + x)
(2(-6 + x) + x(-6 + x)) = (2x + 3)(x + -6)
((-6 * 2 + x * 2) + x(-6 + x)) = (2x + 3)(x + -6)
((-12 + 2x) + x(-6 + x)) = (2x + 3)(x + -6)
(-12 + 2x + (-6 * x + x * x)) = (2x + 3)(x + -6)
(-12 + 2x + (-6x + x2)) = (2x + 3)(x + -6)

Combine like terms: 2x + -6x = -4x
(-12 + -4x + x2) = (2x + 3)(x + -6)

Reorder the terms:
-12 + -4x + x2 = (3 + 2x)(x + -6)

Reorder the terms:
-12 + -4x + x2 = (3 + 2x)(-6 + x)

Multiply (3 + 2x) * (-6 + x)
-12 + -4x + x2 = (3(-6 + x) + 2x * (-6 + x))
-12 + -4x + x2 = ((-6 * 3 + x * 3) + 2x * (-6 + x))
-12 + -4x + x2 = ((-18 + 3x) + 2x * (-6 + x))
-12 + -4x + x2 = (-18 + 3x + (-6 * 2x + x * 2x))
-12 + -4x + x2 = (-18 + 3x + (-12x + 2x2))

Combine like terms: 3x + -12x = -9x
-12 + -4x + x2 = (-18 + -9x + 2x2)

Solving
-12 + -4x + x2 = -18 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-12 + 18 + -4x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: -12 + 18 = 6
6 + -4x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: -4x + 9x = 5x
6 + 5x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
6 + 5x + -1x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Reorder the terms:
6 + 5x + -1x2 = -18 + 18 + -9x + 9x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
6 + 5x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2
6 + 5x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
6 + 5x + -1x2 = 0 + 2x2 + -2x2
6 + 5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + 5x + -1x2 = 0

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


Subproblem 1
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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {6, -1}

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