4x(x+6)=288

Solution for 4x(x+6)=288 equation:

Simplifying
4x(x + 6) = 288

Reorder the terms:
4x(6 + x) = 288
(6 * 4x + x * 4x) = 288
(24x + 4x2) = 288

Solving
24x + 4x2 = 288

Solving for variable 'x'.

Reorder the terms:
-288 + 24x + 4x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 6x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 6}