4(x+2)+(x-3)(x+2)=0

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Solution for 4(x+2)+(x-3)(x+2)=0 equation: 


Simplifying
4(x + 2) + (x + -3)(x + 2) = 0

Reorder the terms:
4(2 + x) + (x + -3)(x + 2) = 0
(2 * 4 + x * 4) + (x + -3)(x + 2) = 0
(8 + 4x) + (x + -3)(x + 2) = 0

Reorder the terms:
8 + 4x + (-3 + x)(x + 2) = 0

Reorder the terms:
8 + 4x + (-3 + x)(2 + x) = 0

Multiply (-3 + x) * (2 + x)
8 + 4x + (-3(2 + x) + x(2 + x)) = 0
8 + 4x + ((2 * -3 + x * -3) + x(2 + x)) = 0
8 + 4x + ((-6 + -3x) + x(2 + x)) = 0
8 + 4x + (-6 + -3x + (2 * x + x * x)) = 0
8 + 4x + (-6 + -3x + (2x + x2)) = 0

Combine like terms: -3x + 2x = -1x
8 + 4x + (-6 + -1x + x2) = 0

Reorder the terms:
8 + -6 + 4x + -1x + x2 = 0

Combine like terms: 8 + -6 = 2
2 + 4x + -1x + x2 = 0

Combine like terms: 4x + -1x = 3x
2 + 3x + x2 = 0

Solving
2 + 3x + x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-2, -1}

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