102=(x+9)(x-2)

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Solution for 102=(x+9)(x-2) equation: 


Simplifying
102 = (x + 9)(x + -2)

Reorder the terms:
102 = (9 + x)(x + -2)

Reorder the terms:
102 = (9 + x)(-2 + x)

Multiply (9 + x) * (-2 + x)
102 = (9(-2 + x) + x(-2 + x))
102 = ((-2 * 9 + x * 9) + x(-2 + x))
102 = ((-18 + 9x) + x(-2 + x))
102 = (-18 + 9x + (-2 * x + x * x))
102 = (-18 + 9x + (-2x + x2))

Combine like terms: 9x + -2x = 7x
102 = (-18 + 7x + x2)

Solving
102 = -18 + 7x + x2

Solving for variable 'x'.

Combine like terms: 102 + 18 = 120
120 + -7x + -1x2 = -18 + 7x + x2 + 18 + -7x + -1x2

Reorder the terms:
120 + -7x + -1x2 = -18 + 18 + 7x + -7x + x2 + -1x2

Combine like terms: -18 + 18 = 0
120 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
120 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
120 + -7x + -1x2 = 0 + x2 + -1x2
120 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
120 + -7x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(15 + 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 '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {8, -15}

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