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

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Solution for 3(x-2)=(x+9)(x-2) equation: 


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

Reorder the terms:
3(-2 + x) = (x + 9)(x + -2)
(-2 * 3 + x * 3) = (x + 9)(x + -2)
(-6 + 3x) = (x + 9)(x + -2)

Reorder the terms:
-6 + 3x = (9 + x)(x + -2)

Reorder the terms:
-6 + 3x = (9 + x)(-2 + x)

Multiply (9 + x) * (-2 + x)
-6 + 3x = (9(-2 + x) + x(-2 + x))
-6 + 3x = ((-2 * 9 + x * 9) + x(-2 + x))
-6 + 3x = ((-18 + 9x) + x(-2 + x))
-6 + 3x = (-18 + 9x + (-2 * x + x * x))
-6 + 3x = (-18 + 9x + (-2x + x2))

Combine like terms: 9x + -2x = 7x
-6 + 3x = (-18 + 7x + x2)

Solving
-6 + 3x = -18 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 18 + 3x + -7x + -1x2 = -18 + 7x + x2 + 18 + -7x + -1x2

Combine like terms: -6 + 18 = 12
12 + 3x + -7x + -1x2 = -18 + 7x + x2 + 18 + -7x + -1x2

Combine like terms: 3x + -7x = -4x
12 + -4x + -1x2 = -18 + 7x + x2 + 18 + -7x + -1x2

Reorder the terms:
12 + -4x + -1x2 = -18 + 18 + 7x + -7x + x2 + -1x2

Combine like terms: -18 + 18 = 0
12 + -4x + -1x2 = 0 + 7x + -7x + x2 + -1x2
12 + -4x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
12 + -4x + -1x2 = 0 + x2 + -1x2
12 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -4x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {2, -6}

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