(2x+4)(2x+6)=48

Solution for (2x+4)(2x+6)=48 equation:

Simplifying
(2x + 4)(2x + 6) = 48

Reorder the terms:
(4 + 2x)(2x + 6) = 48

Reorder the terms:
(4 + 2x)(6 + 2x) = 48

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

Combine like terms: 8x + 12x = 20x
(24 + 20x + 4x2) = 48

Solving
24 + 20x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
24 + -48 + 20x + 4x2 = 48 + -48

Combine like terms: 24 + -48 = -24
-24 + 20x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-24 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 5x + x2) = 0

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

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

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