3x(x-2)-3(x-2)(x+2)=(x+1)(x+2)

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Solution for 3x(x-2)-3(x-2)(x+2)=(x+1)(x+2) equation: 


Simplifying
3x(x + -2) + -3(x + -2)(x + 2) = (x + 1)(x + 2)

Reorder the terms:
3x(-2 + x) + -3(x + -2)(x + 2) = (x + 1)(x + 2)
(-2 * 3x + x * 3x) + -3(x + -2)(x + 2) = (x + 1)(x + 2)
(-6x + 3x2) + -3(x + -2)(x + 2) = (x + 1)(x + 2)

Reorder the terms:
-6x + 3x2 + -3(-2 + x)(x + 2) = (x + 1)(x + 2)

Reorder the terms:
-6x + 3x2 + -3(-2 + x)(2 + x) = (x + 1)(x + 2)

Multiply (-2 + x) * (2 + x)
-6x + 3x2 + -3(-2(2 + x) + x(2 + x)) = (x + 1)(x + 2)
-6x + 3x2 + -3((2 * -2 + x * -2) + x(2 + x)) = (x + 1)(x + 2)
-6x + 3x2 + -3((-4 + -2x) + x(2 + x)) = (x + 1)(x + 2)
-6x + 3x2 + -3(-4 + -2x + (2 * x + x * x)) = (x + 1)(x + 2)
-6x + 3x2 + -3(-4 + -2x + (2x + x2)) = (x + 1)(x + 2)

Combine like terms: -2x + 2x = 0
-6x + 3x2 + -3(-4 + 0 + x2) = (x + 1)(x + 2)
-6x + 3x2 + -3(-4 + x2) = (x + 1)(x + 2)
-6x + 3x2 + (-4 * -3 + x2 * -3) = (x + 1)(x + 2)
-6x + 3x2 + (12 + -3x2) = (x + 1)(x + 2)

Reorder the terms:
12 + -6x + 3x2 + -3x2 = (x + 1)(x + 2)

Combine like terms: 3x2 + -3x2 = 0
12 + -6x + 0 = (x + 1)(x + 2)
12 + -6x = (x + 1)(x + 2)

Reorder the terms:
12 + -6x = (1 + x)(x + 2)

Reorder the terms:
12 + -6x = (1 + x)(2 + x)

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

Combine like terms: 1x + 2x = 3x
12 + -6x = (2 + 3x + x2)

Solving
12 + -6x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -2 + -6x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 12 + -2 = 10
10 + -6x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: -6x + -3x = -9x
10 + -9x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
10 + -9x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
10 + -9x + -1x2 = 0 + 3x + -3x + x2 + -1x2
10 + -9x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
10 + -9x + -1x2 = 0 + x2 + -1x2
10 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -9x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {1, -10}

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