(x+3)(x-6)=(2x+4)(x-6)

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Solution for (x+3)(x-6)=(2x+4)(x-6) equation: 


Simplifying
(x + 3)(x + -6) = (2x + 4)(x + -6)

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

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

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

Combine like terms: 3x + -6x = -3x
(-18 + -3x + x2) = (2x + 4)(x + -6)

Reorder the terms:
-18 + -3x + x2 = (4 + 2x)(x + -6)

Reorder the terms:
-18 + -3x + x2 = (4 + 2x)(-6 + x)

Multiply (4 + 2x) * (-6 + x)
-18 + -3x + x2 = (4(-6 + x) + 2x * (-6 + x))
-18 + -3x + x2 = ((-6 * 4 + x * 4) + 2x * (-6 + x))
-18 + -3x + x2 = ((-24 + 4x) + 2x * (-6 + x))
-18 + -3x + x2 = (-24 + 4x + (-6 * 2x + x * 2x))
-18 + -3x + x2 = (-24 + 4x + (-12x + 2x2))

Combine like terms: 4x + -12x = -8x
-18 + -3x + x2 = (-24 + -8x + 2x2)

Solving
-18 + -3x + x2 = -24 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 24 + -3x + 8x + x2 + -2x2 = -24 + -8x + 2x2 + 24 + 8x + -2x2

Combine like terms: -18 + 24 = 6
6 + -3x + 8x + x2 + -2x2 = -24 + -8x + 2x2 + 24 + 8x + -2x2

Combine like terms: -3x + 8x = 5x
6 + 5x + x2 + -2x2 = -24 + -8x + 2x2 + 24 + 8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
6 + 5x + -1x2 = -24 + -8x + 2x2 + 24 + 8x + -2x2

Reorder the terms:
6 + 5x + -1x2 = -24 + 24 + -8x + 8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
6 + 5x + -1x2 = 0 + -8x + 8x + 2x2 + -2x2
6 + 5x + -1x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 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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