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

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


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

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

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

Multiply (4 + 2x) * (3 + x)
0 = (4(3 + x) + 2x * (3 + x))
0 = ((3 * 4 + x * 4) + 2x * (3 + x))
0 = ((12 + 4x) + 2x * (3 + x))
0 = (12 + 4x + (3 * 2x + x * 2x))
0 = (12 + 4x + (6x + 2x2))

Combine like terms: 4x + 6x = 10x
0 = (12 + 10x + 2x2)

Solving
0 = 12 + 10x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -10x + -2x2 = 12 + 10x + 2x2 + -12 + -10x + -2x2

Reorder the terms:
-12 + -10x + -2x2 = 12 + -12 + 10x + -10x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
-12 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2
-12 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-12 + -10x + -2x2 = 0 + 2x2 + -2x2
-12 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(6 + 5x + x2) = 0

Factor a trinomial.
-2((3 + x)(2 + x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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 = {-3, -2}

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