12x(x-1)=36-x

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Solution for 12x(x-1)=36-x equation: 


Simplifying
12x(x + -1) = 36 + -1x

Reorder the terms:
12x(-1 + x) = 36 + -1x
(-1 * 12x + x * 12x) = 36 + -1x
(-12x + 12x2) = 36 + -1x

Solving
-12x + 12x2 = 36 + -1x

Solving for variable 'x'.

Reorder the terms:
-36 + -12x + x + 12x2 = 36 + -1x + -36 + x

Combine like terms: -12x + x = -11x
-36 + -11x + 12x2 = 36 + -1x + -36 + x

Reorder the terms:
-36 + -11x + 12x2 = 36 + -36 + -1x + x

Combine like terms: 36 + -36 = 0
-36 + -11x + 12x2 = 0 + -1x + x
-36 + -11x + 12x2 = -1x + x

Combine like terms: -1x + x = 0
-36 + -11x + 12x2 = 0

Factor a trinomial.
(-4 + -3x)(9 + -4x) = 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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-1.333333333, 2.25}

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