x(x-6)=7x-12

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Solution for x(x-6)=7x-12 equation: 


Simplifying
x(x + -6) = 7x + -12

Reorder the terms:
x(-6 + x) = 7x + -12
(-6 * x + x * x) = 7x + -12
(-6x + x2) = 7x + -12

Reorder the terms:
-6x + x2 = -12 + 7x

Solving
-6x + x2 = -12 + 7x

Solving for variable 'x'.

Reorder the terms:
12 + -6x + -7x + x2 = -12 + 7x + 12 + -7x

Combine like terms: -6x + -7x = -13x
12 + -13x + x2 = -12 + 7x + 12 + -7x

Reorder the terms:
12 + -13x + x2 = -12 + 12 + 7x + -7x

Combine like terms: -12 + 12 = 0
12 + -13x + x2 = 0 + 7x + -7x
12 + -13x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
12 + -13x + x2 = 0

Factor a trinomial.
(1 + -1x)(12 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {1, 12}

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