6x^2-24x=-32

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Solution for 6x^2-24x=-32 equation: 


Simplifying
6x2 + -24x = -32

Reorder the terms:
-24x + 6x2 = -32

Solving
-24x + 6x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -24x + 6x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
16 + -12x + 3x2 = 0

Solving
16 + -12x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -4x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -4x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -5.333333333
-4x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-4x + x2 = -5.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -5.333333333 + 4

Reorder the terms:
4 + -4x + x2 = -5.333333333 + 4

Combine like terms: -5.333333333 + 4 = -1.333333333
4 + -4x + x2 = -1.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = -1.333333333

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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