6x^2-9x=8x-12

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Solution for 6x^2-9x=8x-12 equation: 


Simplifying
6x2 + -9x = 8x + -12

Reorder the terms:
-9x + 6x2 = 8x + -12

Reorder the terms:
-9x + 6x2 = -12 + 8x

Solving
-9x + 6x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
12 + -9x + -8x + 6x2 = -12 + 8x + 12 + -8x

Combine like terms: -9x + -8x = -17x
12 + -17x + 6x2 = -12 + 8x + 12 + -8x

Reorder the terms:
12 + -17x + 6x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
12 + -17x + 6x2 = 0 + 8x + -8x
12 + -17x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
12 + -17x + 6x2 = 0

Factor a trinomial.
(4 + -3x)(3 + -2x) = 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 + -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
Solution
x = {1.333333333, 1.5}

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