4x(x+4)=48

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

Simplifying
4x(x + 4) = 48

Reorder the terms:
4x(4 + x) = 48
(4 * 4x + x * 4x) = 48
(16x + 4x2) = 48

Solving
16x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 16x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 4x + x2) = 0

Factor a trinomial.
4((-6 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}