9x=(x+4)(x-2)

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Solution for 9x=(x+4)(x-2) equation: 


Simplifying
9x = (x + 4)(x + -2)

Reorder the terms:
9x = (4 + x)(x + -2)

Reorder the terms:
9x = (4 + x)(-2 + x)

Multiply (4 + x) * (-2 + x)
9x = (4(-2 + x) + x(-2 + x))
9x = ((-2 * 4 + x * 4) + x(-2 + x))
9x = ((-8 + 4x) + x(-2 + x))
9x = (-8 + 4x + (-2 * x + x * x))
9x = (-8 + 4x + (-2x + x2))

Combine like terms: 4x + -2x = 2x
9x = (-8 + 2x + x2)

Solving
9x = -8 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
8 + 9x + -2x + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: 9x + -2x = 7x
8 + 7x + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Reorder the terms:
8 + 7x + -1x2 = -8 + 8 + 2x + -2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
8 + 7x + -1x2 = 0 + 2x + -2x + x2 + -1x2
8 + 7x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
8 + 7x + -1x2 = 0 + x2 + -1x2
8 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 7x + -1x2 = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {8, -1}

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