(2x+4)(x-1)+(x+2)(x+2)=0

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Solution for (2x+4)(x-1)+(x+2)(x+2)=0 equation: 


Simplifying
(2x + 4)(x + -1) + (x + 2)(x + 2) = 0

Reorder the terms:
(4 + 2x)(x + -1) + (x + 2)(x + 2) = 0

Reorder the terms:
(4 + 2x)(-1 + x) + (x + 2)(x + 2) = 0

Multiply (4 + 2x) * (-1 + x)
(4(-1 + x) + 2x * (-1 + x)) + (x + 2)(x + 2) = 0
((-1 * 4 + x * 4) + 2x * (-1 + x)) + (x + 2)(x + 2) = 0
((-4 + 4x) + 2x * (-1 + x)) + (x + 2)(x + 2) = 0
(-4 + 4x + (-1 * 2x + x * 2x)) + (x + 2)(x + 2) = 0
(-4 + 4x + (-2x + 2x2)) + (x + 2)(x + 2) = 0

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

Reorder the terms:
-4 + 2x + 2x2 + (2 + x)(x + 2) = 0

Reorder the terms:
-4 + 2x + 2x2 + (2 + x)(2 + x) = 0

Multiply (2 + x) * (2 + x)
-4 + 2x + 2x2 + (2(2 + x) + x(2 + x)) = 0
-4 + 2x + 2x2 + ((2 * 2 + x * 2) + x(2 + x)) = 0
-4 + 2x + 2x2 + ((4 + 2x) + x(2 + x)) = 0
-4 + 2x + 2x2 + (4 + 2x + (2 * x + x * x)) = 0
-4 + 2x + 2x2 + (4 + 2x + (2x + x2)) = 0

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

Reorder the terms:
-4 + 4 + 2x + 4x + 2x2 + x2 = 0

Combine like terms: -4 + 4 = 0
0 + 2x + 4x + 2x2 + x2 = 0
2x + 4x + 2x2 + x2 = 0

Combine like terms: 2x + 4x = 6x
6x + 2x2 + x2 = 0

Combine like terms: 2x2 + x2 = 3x2
6x + 3x2 = 0

Solving
6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2 + x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, -2}

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