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

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


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

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

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

Multiply (-2 + x) * (7 + x)
90 = (-2(7 + x) + x(7 + x))
90 = ((7 * -2 + x * -2) + x(7 + x))
90 = ((-14 + -2x) + x(7 + x))
90 = (-14 + -2x + (7 * x + x * x))
90 = (-14 + -2x + (7x + x2))

Combine like terms: -2x + 7x = 5x
90 = (-14 + 5x + x2)

Solving
90 = -14 + 5x + x2

Solving for variable 'x'.

Combine like terms: 90 + 14 = 104
104 + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
104 + -5x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
104 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
104 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
104 + -5x + -1x2 = 0 + x2 + -1x2
104 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
104 + -5x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(13 + x) = 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 '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 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 + x = 0 + -13

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

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

Simplifying
x = -13
Solution
x = {8, -13}

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