8x^2-16x=6x-12

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Solution for 8x^2-16x=6x-12 equation: 


Simplifying
8x2 + -16x = 6x + -12

Reorder the terms:
-16x + 8x2 = 6x + -12

Reorder the terms:
-16x + 8x2 = -12 + 6x

Solving
-16x + 8x2 = -12 + 6x

Solving for variable 'x'.

Reorder the terms:
12 + -16x + -6x + 8x2 = -12 + 6x + 12 + -6x

Combine like terms: -16x + -6x = -22x
12 + -22x + 8x2 = -12 + 6x + 12 + -6x

Reorder the terms:
12 + -22x + 8x2 = -12 + 12 + 6x + -6x

Combine like terms: -12 + 12 = 0
12 + -22x + 8x2 = 0 + 6x + -6x
12 + -22x + 8x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -22x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11x + 4x2) = 0

Factor a trinomial.
2((3 + -4x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
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
Solution
x = {0.75, 2}

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