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

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


Simplifying
(2x + 4)(2x + 3) + -1(2x + 4) = 0

Reorder the terms:
(4 + 2x)(2x + 3) + -1(2x + 4) = 0

Reorder the terms:
(4 + 2x)(3 + 2x) + -1(2x + 4) = 0

Multiply (4 + 2x) * (3 + 2x)
(4(3 + 2x) + 2x * (3 + 2x)) + -1(2x + 4) = 0
((3 * 4 + 2x * 4) + 2x * (3 + 2x)) + -1(2x + 4) = 0
((12 + 8x) + 2x * (3 + 2x)) + -1(2x + 4) = 0
(12 + 8x + (3 * 2x + 2x * 2x)) + -1(2x + 4) = 0
(12 + 8x + (6x + 4x2)) + -1(2x + 4) = 0

Combine like terms: 8x + 6x = 14x
(12 + 14x + 4x2) + -1(2x + 4) = 0

Reorder the terms:
12 + 14x + 4x2 + -1(4 + 2x) = 0
12 + 14x + 4x2 + (4 * -1 + 2x * -1) = 0
12 + 14x + 4x2 + (-4 + -2x) = 0

Reorder the terms:
12 + -4 + 14x + -2x + 4x2 = 0

Combine like terms: 12 + -4 = 8
8 + 14x + -2x + 4x2 = 0

Combine like terms: 14x + -2x = 12x
8 + 12x + 4x2 = 0

Solving
8 + 12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3x + x2) = 0

Factor a trinomial.
4((2 + x)(1 + x)) = 0

Ignore the factor 4.

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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