(6+2x)(4+2x)-24=39

Solution for (6+2x)(4+2x)-24=39 equation:

Simplifying
(6 + 2x)(4 + 2x) + -24 = 39

Multiply (6 + 2x) * (4 + 2x)
(6(4 + 2x) + 2x * (4 + 2x)) + -24 = 39
((4 * 6 + 2x * 6) + 2x * (4 + 2x)) + -24 = 39
((24 + 12x) + 2x * (4 + 2x)) + -24 = 39
(24 + 12x + (4 * 2x + 2x * 2x)) + -24 = 39
(24 + 12x + (8x + 4x2)) + -24 = 39

Combine like terms: 12x + 8x = 20x
(24 + 20x + 4x2) + -24 = 39

Reorder the terms:
24 + -24 + 20x + 4x2 = 39

Combine like terms: 24 + -24 = 0
0 + 20x + 4x2 = 39
20x + 4x2 = 39

Solving
20x + 4x2 = 39

Solving for variable 'x'.

Reorder the terms:
-39 + 20x + 4x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + 20x + 4x2 = 0

Factor a trinomial.
(-13 + -2x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-6.5, 1.5}