x(6x-2)=-24

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Solution for x(6x-2)=-24 equation: 


Simplifying
x(6x + -2) = -24

Reorder the terms:
x(-2 + 6x) = -24
(-2 * x + 6x * x) = -24
(-2x + 6x2) = -24

Solving
-2x + 6x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + -2x + 6x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -1x + 3x2) = 0

Ignore the factor 2.

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

Simplifying
12 + -1x + 3x2 = 0

Solving
12 + -1x + 3x2 = 0

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

Divide each side by '3'.
4 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -0.3333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -0.3333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -0.3333333333x + x2 = 0 + -4
-0.3333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-0.3333333333x + x2 = -4

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = -4 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = -4 + 0.02777777779

Combine like terms: -4 + 0.02777777779 = -3.97222222221
0.02777777779 + -0.3333333333x + x2 = -3.97222222221

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = -3.97222222221

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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