(x+2)(2x+3)=91

Solution for (x+2)(2x+3)=91 equation:

Simplifying
(x + 2)(2x + 3) = 91

Reorder the terms:
(2 + x)(2x + 3) = 91

Reorder the terms:
(2 + x)(3 + 2x) = 91

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = 91
((3 * 2 + 2x * 2) + x(3 + 2x)) = 91
((6 + 4x) + x(3 + 2x)) = 91
(6 + 4x + (3 * x + 2x * x)) = 91
(6 + 4x + (3x + 2x2)) = 91

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = 91

Solving
6 + 7x + 2x2 = 91

Solving for variable 'x'.

Reorder the terms:
6 + -91 + 7x + 2x2 = 91 + -91

Combine like terms: 6 + -91 = -85
-85 + 7x + 2x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-85 + 7x + 2x2 = 0

Factor a trinomial.
(-17 + -2x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve:

Simplifying
-17 + -2x = 0

Solving
-17 + -2x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -2x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2x = 0 + 17
-2x = 0 + 17

Combine like terms: 0 + 17 = 17
-2x = 17

Divide each side by '-2'.
x = -8.5

Simplifying
x = -8.5
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 = {-8.5, 5}