0=(4+2x)(6+2x)-24

Solution for 0=(4+2x)(6+2x)-24 equation:

Simplifying
0 = (4 + 2x)(6 + 2x) + -24

Multiply (4 + 2x) * (6 + 2x)
0 = (4(6 + 2x) + 2x * (6 + 2x)) + -24
0 = ((6 * 4 + 2x * 4) + 2x * (6 + 2x)) + -24
0 = ((24 + 8x) + 2x * (6 + 2x)) + -24
0 = (24 + 8x + (6 * 2x + 2x * 2x)) + -24
0 = (24 + 8x + (12x + 4x2)) + -24

Combine like terms: 8x + 12x = 20x
0 = (24 + 20x + 4x2) + -24

Reorder the terms:
0 = 24 + -24 + 20x + 4x2

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

Solving
0 = 20x + 4x2

Solving for variable 'x'.
Remove the zero:
-20x + -4x2 = 20x + 4x2 + -20x + -4x2

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

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

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

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(5 + x) = 0

Ignore the factor -4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}