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

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

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

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

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

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

Combine like terms: 2x + 1x = 3x
(1 + 3x + 2x2) = 91

Solving
1 + 3x + 2x2 = 91

Solving for variable 'x'.

Reorder the terms:
1 + -91 + 3x + 2x2 = 91 + -91

Combine like terms: 1 + -91 = -90
-90 + 3x + 2x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-90 + 3x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7.5, 6}