91=(2x+3)(x+1)

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Solution for 91=(2x+3)(x+1) equation: 


Simplifying
91 = (2x + 3)(x + 1)

Reorder the terms:
91 = (3 + 2x)(x + 1)

Reorder the terms:
91 = (3 + 2x)(1 + x)

Multiply (3 + 2x) * (1 + x)
91 = (3(1 + x) + 2x * (1 + x))
91 = ((1 * 3 + x * 3) + 2x * (1 + x))
91 = ((3 + 3x) + 2x * (1 + x))
91 = (3 + 3x + (1 * 2x + x * 2x))
91 = (3 + 3x + (2x + 2x2))

Combine like terms: 3x + 2x = 5x
91 = (3 + 5x + 2x2)

Solving
91 = 3 + 5x + 2x2

Solving for variable 'x'.

Combine like terms: 91 + -3 = 88
88 + -5x + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2

Reorder the terms:
88 + -5x + -2x2 = 3 + -3 + 5x + -5x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
88 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
88 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
88 + -5x + -2x2 = 0 + 2x2 + -2x2
88 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
88 + -5x + -2x2 = 0

Factor a trinomial.
(11 + -2x)(8 + x) = 0


Subproblem 1
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {5.5, -8}

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