(2x+3)(x+4)=88

Solution for (2x+3)(x+4)=88 equation:

Simplifying
(2x + 3)(x + 4) = 88

Reorder the terms:
(3 + 2x)(x + 4) = 88

Reorder the terms:
(3 + 2x)(4 + x) = 88

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x)) = 88
((4 * 3 + x * 3) + 2x * (4 + x)) = 88
((12 + 3x) + 2x * (4 + x)) = 88
(12 + 3x + (4 * 2x + x * 2x)) = 88
(12 + 3x + (8x + 2x2)) = 88

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2) = 88

Solving
12 + 11x + 2x2 = 88

Solving for variable 'x'.

Reorder the terms:
12 + -88 + 11x + 2x2 = 88 + -88

Combine like terms: 12 + -88 = -76
-76 + 11x + 2x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-76 + 11x + 2x2 = 0

Factor a trinomial.
(-19 + -2x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5
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 = {-9.5, 4}