(2x+12)(x+9)=3608

Solution for (2x+12)(x+9)=3608 equation:

Simplifying
(2x + 12)(x + 9) = 3608

Reorder the terms:
(12 + 2x)(x + 9) = 3608

Reorder the terms:
(12 + 2x)(9 + x) = 3608

Multiply (12 + 2x) * (9 + x)
(12(9 + x) + 2x * (9 + x)) = 3608
((9 * 12 + x * 12) + 2x * (9 + x)) = 3608
((108 + 12x) + 2x * (9 + x)) = 3608
(108 + 12x + (9 * 2x + x * 2x)) = 3608
(108 + 12x + (18x + 2x2)) = 3608

Combine like terms: 12x + 18x = 30x
(108 + 30x + 2x2) = 3608

Solving
108 + 30x + 2x2 = 3608

Solving for variable 'x'.

Reorder the terms:
108 + -3608 + 30x + 2x2 = 3608 + -3608

Combine like terms: 108 + -3608 = -3500
-3500 + 30x + 2x2 = 3608 + -3608

Combine like terms: 3608 + -3608 = 0
-3500 + 30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1750 + 15x + x2) = 0

Factor a trinomial.
2((-50 + -1x)(35 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Solution
x = {-50, 35}