x(x-1)=3x+12

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Solution for x(x-1)=3x+12 equation:


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

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

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

Solving
-1x + x2 = 12 + 3x

Solving for variable 'x'.

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

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

Reorder the terms:
-12 + -4x + x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + -4x + x2 = 0 + 3x + -3x
-12 + -4x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

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

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