12x-6x^2=10

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Solution for 12x-6x^2=10 equation: 


Simplifying
12x + -6x2 = 10

Solving
12x + -6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + -6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 6x + -3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 6x + -3x2 = 0

Solving
-5 + 6x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -2x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -2x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + -1.666666667
-2x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-2x + x2 = -1.666666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -1.666666667 + 1

Reorder the terms:
1 + -2x + x2 = -1.666666667 + 1

Combine like terms: -1.666666667 + 1 = -0.666666667
1 + -2x + x2 = -0.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = -0.666666667

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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