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

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


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

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

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

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

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

Solving
-8 + 2x + x2 = 9x

Solving for variable 'x'.

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

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

Combine like terms: 9x + -9x = 0
-8 + -7x + x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -1x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, 8}

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