3x(x-2)=12-x

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Solution for 3x(x-2)=12-x equation: 


Simplifying
3x(x + -2) = 12 + -1x

Reorder the terms:
3x(-2 + x) = 12 + -1x
(-2 * 3x + x * 3x) = 12 + -1x
(-6x + 3x2) = 12 + -1x

Solving
-6x + 3x2 = 12 + -1x

Solving for variable 'x'.

Reorder the terms:
-12 + -6x + x + 3x2 = 12 + -1x + -12 + x

Combine like terms: -6x + x = -5x
-12 + -5x + 3x2 = 12 + -1x + -12 + x

Reorder the terms:
-12 + -5x + 3x2 = 12 + -12 + -1x + x

Combine like terms: 12 + -12 = 0
-12 + -5x + 3x2 = 0 + -1x + x
-12 + -5x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
-12 + -5x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.333333333, 3}

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