(x+4)(2x+3)=117

Solution for (x+4)(2x+3)=117 equation:

Simplifying
(x + 4)(2x + 3) = 117

Reorder the terms:
(4 + x)(2x + 3) = 117

Reorder the terms:
(4 + x)(3 + 2x) = 117

Multiply (4 + x) * (3 + 2x)
(4(3 + 2x) + x(3 + 2x)) = 117
((3 * 4 + 2x * 4) + x(3 + 2x)) = 117
((12 + 8x) + x(3 + 2x)) = 117
(12 + 8x + (3 * x + 2x * x)) = 117
(12 + 8x + (3x + 2x2)) = 117

Combine like terms: 8x + 3x = 11x
(12 + 11x + 2x2) = 117

Solving
12 + 11x + 2x2 = 117

Solving for variable 'x'.

Reorder the terms:
12 + -117 + 11x + 2x2 = 117 + -117

Combine like terms: 12 + -117 = -105
-105 + 11x + 2x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-105 + 11x + 2x2 = 0

Factor a trinomial.
(-21 + -2x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve:

Simplifying
-21 + -2x = 0

Solving
-21 + -2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2x = 0 + 21
-2x = 0 + 21

Combine like terms: 0 + 21 = 21
-2x = 21

Divide each side by '-2'.
x = -10.5

Simplifying
x = -10.5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-10.5, 5}