(2x+1)(x)=91

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

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

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

Reorder the terms for easier multiplication:
x(1 + 2x) = 91
(1 * x + 2x * x) = 91
(1x + 2x2) = 91

Solving
1x + 2x2 = 91

Solving for variable 'x'.

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

Combine like terms: 91 + -91 = 0
-91 + 1x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(13 + -2x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {-7, 6.5}