(2x+1)(x+2)=90

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Solution for (2x+1)(x+2)=90 equation: 


Simplifying
(2x + 1)(x + 2) = 90

Reorder the terms:
(1 + 2x)(x + 2) = 90

Reorder the terms:
(1 + 2x)(2 + x) = 90

Multiply (1 + 2x) * (2 + x)
(1(2 + x) + 2x * (2 + x)) = 90
((2 * 1 + x * 1) + 2x * (2 + x)) = 90
((2 + 1x) + 2x * (2 + x)) = 90
(2 + 1x + (2 * 2x + x * 2x)) = 90
(2 + 1x + (4x + 2x2)) = 90

Combine like terms: 1x + 4x = 5x
(2 + 5x + 2x2) = 90

Solving
2 + 5x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
2 + -90 + 5x + 2x2 = 90 + -90

Combine like terms: 2 + -90 = -88
-88 + 5x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-88 + 5x + 2x2 = 0

Factor a trinomial.
(-8 + -1x)(11 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
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
Solution
x = {-8, 5.5}

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