(8+2x)(6+2x)=24

Solution for (8+2x)(6+2x)=24 equation:

Simplifying
(8 + 2x)(6 + 2x) = 24

Multiply (8 + 2x) * (6 + 2x)
(8(6 + 2x) + 2x * (6 + 2x)) = 24
((6 * 8 + 2x * 8) + 2x * (6 + 2x)) = 24
((48 + 16x) + 2x * (6 + 2x)) = 24
(48 + 16x + (6 * 2x + 2x * 2x)) = 24
(48 + 16x + (12x + 4x2)) = 24

Combine like terms: 16x + 12x = 28x
(48 + 28x + 4x2) = 24

Solving
48 + 28x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
48 + -24 + 28x + 4x2 = 24 + -24

Combine like terms: 48 + -24 = 24
24 + 28x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
24 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 7x + x2) = 0

Factor a trinomial.
4((6 + x)(1 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
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 = {-6, -1}