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

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


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

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

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

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

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

Solving
91 = 1 + 3x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
90 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
90 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
90 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {6, -7.5}

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