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

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

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

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

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

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

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

Solving
91 = 6 + 7x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
85 + -7x + -2x2 = 6 + -6 + 7x + -7x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
85 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2
85 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {5, -8.5}