(2x+3)(2x+4)=20

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Solution for (2x+3)(2x+4)=20 equation: 


Simplifying
(2x + 3)(2x + 4) = 20

Reorder the terms:
(3 + 2x)(2x + 4) = 20

Reorder the terms:
(3 + 2x)(4 + 2x) = 20

Multiply (3 + 2x) * (4 + 2x)
(3(4 + 2x) + 2x * (4 + 2x)) = 20
((4 * 3 + 2x * 3) + 2x * (4 + 2x)) = 20
((12 + 6x) + 2x * (4 + 2x)) = 20
(12 + 6x + (4 * 2x + 2x * 2x)) = 20
(12 + 6x + (8x + 4x2)) = 20

Combine like terms: 6x + 8x = 14x
(12 + 14x + 4x2) = 20

Solving
12 + 14x + 4x2 = 20

Solving for variable 'x'.

Reorder the terms:
12 + -20 + 14x + 4x2 = 20 + -20

Combine like terms: 12 + -20 = -8
-8 + 14x + 4x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-8 + 14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 7x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4, 0.5}

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