4x(x+9)=208

Solution for 4x(x+9)=208 equation:

Simplifying
4x(x + 9) = 208

Reorder the terms:
4x(9 + x) = 208
(9 * 4x + x * 4x) = 208
(36x + 4x2) = 208

Solving
36x + 4x2 = 208

Solving for variable 'x'.

Reorder the terms:
-208 + 36x + 4x2 = 208 + -208

Combine like terms: 208 + -208 = 0
-208 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-52 + 9x + x2) = 0

Factor a trinomial.
4((-13 + -1x)(4 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-13, 4}