90=(2x+7)(2x+6)

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Solution for 90=(2x+7)(2x+6) equation: 


Simplifying
90 = (2x + 7)(2x + 6)

Reorder the terms:
90 = (7 + 2x)(2x + 6)

Reorder the terms:
90 = (7 + 2x)(6 + 2x)

Multiply (7 + 2x) * (6 + 2x)
90 = (7(6 + 2x) + 2x * (6 + 2x))
90 = ((6 * 7 + 2x * 7) + 2x * (6 + 2x))
90 = ((42 + 14x) + 2x * (6 + 2x))
90 = (42 + 14x + (6 * 2x + 2x * 2x))
90 = (42 + 14x + (12x + 4x2))

Combine like terms: 14x + 12x = 26x
90 = (42 + 26x + 4x2)

Solving
90 = 42 + 26x + 4x2

Solving for variable 'x'.

Combine like terms: 90 + -42 = 48
48 + -26x + -4x2 = 42 + 26x + 4x2 + -42 + -26x + -4x2

Reorder the terms:
48 + -26x + -4x2 = 42 + -42 + 26x + -26x + 4x2 + -4x2

Combine like terms: 42 + -42 = 0
48 + -26x + -4x2 = 0 + 26x + -26x + 4x2 + -4x2
48 + -26x + -4x2 = 26x + -26x + 4x2 + -4x2

Combine like terms: 26x + -26x = 0
48 + -26x + -4x2 = 0 + 4x2 + -4x2
48 + -26x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
48 + -26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -13x + -2x2) = 0

Factor a trinomial.
2((3 + -2x)(8 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

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

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

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

Simplifying
x = -8
Solution
x = {1.5, -8}

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