-2x-x+12=-3x^2+6x

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Solution for -2x-x+12=-3x^2+6x equation: 


Simplifying
-2x + -1x + 12 = -3x2 + 6x

Reorder the terms:
12 + -2x + -1x = -3x2 + 6x

Combine like terms: -2x + -1x = -3x
12 + -3x = -3x2 + 6x

Reorder the terms:
12 + -3x = 6x + -3x2

Solving
12 + -3x = 6x + -3x2

Solving for variable 'x'.

Combine like terms: -3x + -6x = -9x
12 + -9x + 3x2 = 6x + -3x2 + -6x + 3x2

Reorder the terms:
12 + -9x + 3x2 = 6x + -6x + -3x2 + 3x2

Combine like terms: 6x + -6x = 0
12 + -9x + 3x2 = 0 + -3x2 + 3x2
12 + -9x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x + x2 = 0

Solving
4 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -3x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -3x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x + x2 = 0 + -4
-3x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x + x2 = -4

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -4 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + -3x + x2 = -1.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -1.75

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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