(x+2)(x+1)=(2x+4)(x-2)

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Solution for (x+2)(x+1)=(2x+4)(x-2) equation: 


Simplifying
(x + 2)(x + 1) = (2x + 4)(x + -2)

Reorder the terms:
(2 + x)(x + 1) = (2x + 4)(x + -2)

Reorder the terms:
(2 + x)(1 + x) = (2x + 4)(x + -2)

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

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = (2x + 4)(x + -2)

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

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

Multiply (4 + 2x) * (-2 + x)
2 + 3x + x2 = (4(-2 + x) + 2x * (-2 + x))
2 + 3x + x2 = ((-2 * 4 + x * 4) + 2x * (-2 + x))
2 + 3x + x2 = ((-8 + 4x) + 2x * (-2 + x))
2 + 3x + x2 = (-8 + 4x + (-2 * 2x + x * 2x))
2 + 3x + x2 = (-8 + 4x + (-4x + 2x2))

Combine like terms: 4x + -4x = 0
2 + 3x + x2 = (-8 + 0 + 2x2)
2 + 3x + x2 = (-8 + 2x2)

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

Solving for variable 'x'.

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

Combine like terms: 2 + 8 = 10
10 + 3x + x2 + -2x2 = -8 + 2x2 + 8 + -2x2

Combine like terms: x2 + -2x2 = -1x2
10 + 3x + -1x2 = -8 + 2x2 + 8 + -2x2

Reorder the terms:
10 + 3x + -1x2 = -8 + 8 + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
10 + 3x + -1x2 = 0 + 2x2 + -2x2
10 + 3x + -1x2 = 2x2 + -2x2

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

Factor a trinomial.
(5 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {5, -2}

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