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

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


Simplifying
2x2 + -6x + 8 = 6x + -12

Reorder the terms:
8 + -6x + 2x2 = 6x + -12

Reorder the terms:
8 + -6x + 2x2 = -12 + 6x

Solving
8 + -6x + 2x2 = -12 + 6x

Solving for variable 'x'.

Reorder the terms:
8 + 12 + -6x + -6x + 2x2 = -12 + 6x + 12 + -6x

Combine like terms: 8 + 12 = 20
20 + -6x + -6x + 2x2 = -12 + 6x + 12 + -6x

Combine like terms: -6x + -6x = -12x
20 + -12x + 2x2 = -12 + 6x + 12 + -6x

Reorder the terms:
20 + -12x + 2x2 = -12 + 12 + 6x + -6x

Combine like terms: -12 + 12 = 0
20 + -12x + 2x2 = 0 + 6x + -6x
20 + -12x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
20 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -6x + x2 = 0

Solving
10 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -6x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -6x + x2 = 0 + -10
-6x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-6x + x2 = -10

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -10 + 9

Reorder the terms:
9 + -6x + x2 = -10 + 9

Combine like terms: -10 + 9 = -1
9 + -6x + x2 = -1

Factor a perfect square on the left side:
(x + -3)(x + -3) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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