3(x^2-6)+3x=x(x-2)

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Solution for 3(x^2-6)+3x=x(x-2) equation: 


Simplifying
3(x2 + -6) + 3x = x(x + -2)

Reorder the terms:
3(-6 + x2) + 3x = x(x + -2)
(-6 * 3 + x2 * 3) + 3x = x(x + -2)
(-18 + 3x2) + 3x = x(x + -2)

Reorder the terms:
-18 + 3x + 3x2 = x(x + -2)

Reorder the terms:
-18 + 3x + 3x2 = x(-2 + x)
-18 + 3x + 3x2 = (-2 * x + x * x)
-18 + 3x + 3x2 = (-2x + x2)

Solving
-18 + 3x + 3x2 = -2x + x2

Solving for variable 'x'.

Reorder the terms:
-18 + 3x + 2x + 3x2 + -1x2 = -2x + x2 + 2x + -1x2

Combine like terms: 3x + 2x = 5x
-18 + 5x + 3x2 + -1x2 = -2x + x2 + 2x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-18 + 5x + 2x2 = -2x + x2 + 2x + -1x2

Reorder the terms:
-18 + 5x + 2x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-18 + 5x + 2x2 = 0 + x2 + -1x2
-18 + 5x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 5x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
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
Solution
x = {-4.5, 2}

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