(2x+4)(2x+5)=90

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Solution for (2x+4)(2x+5)=90 equation: 


Simplifying
(2x + 4)(2x + 5) = 90

Reorder the terms:
(4 + 2x)(2x + 5) = 90

Reorder the terms:
(4 + 2x)(5 + 2x) = 90

Multiply (4 + 2x) * (5 + 2x)
(4(5 + 2x) + 2x * (5 + 2x)) = 90
((5 * 4 + 2x * 4) + 2x * (5 + 2x)) = 90
((20 + 8x) + 2x * (5 + 2x)) = 90
(20 + 8x + (5 * 2x + 2x * 2x)) = 90
(20 + 8x + (10x + 4x2)) = 90

Combine like terms: 8x + 10x = 18x
(20 + 18x + 4x2) = 90

Solving
20 + 18x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
20 + -90 + 18x + 4x2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + 18x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 9x + 2x2) = 0

Factor a trinomial.
2((-7 + -1x)(5 + -2x)) = 0

Ignore the factor 2.

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-7, 2.5}

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