6x(x-1)=12-7x

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Solution for 6x(x-1)=12-7x equation: 


Simplifying
6x(x + -1) = 12 + -7x

Reorder the terms:
6x(-1 + x) = 12 + -7x
(-1 * 6x + x * 6x) = 12 + -7x
(-6x + 6x2) = 12 + -7x

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

Solving for variable 'x'.

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

Combine like terms: -6x + 7x = 1x
-12 + 1x + 6x2 = 12 + -7x + -12 + 7x

Reorder the terms:
-12 + 1x + 6x2 = 12 + -12 + -7x + 7x

Combine like terms: 12 + -12 = 0
-12 + 1x + 6x2 = 0 + -7x + 7x
-12 + 1x + 6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-12 + 1x + 6x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -3x) = 0


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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 1.333333333}

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