8x(6-3x)=4-8(-12x-6)

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Solution for 8x(6-3x)=4-8(-12x-6) equation: 


Simplifying
8x(6 + -3x) = 4 + -8(-12x + -6)
(6 * 8x + -3x * 8x) = 4 + -8(-12x + -6)
(48x + -24x2) = 4 + -8(-12x + -6)

Reorder the terms:
48x + -24x2 = 4 + -8(-6 + -12x)
48x + -24x2 = 4 + (-6 * -8 + -12x * -8)
48x + -24x2 = 4 + (48 + 96x)

Combine like terms: 4 + 48 = 52
48x + -24x2 = 52 + 96x

Solving
48x + -24x2 = 52 + 96x

Solving for variable 'x'.

Reorder the terms:
-52 + 48x + -96x + -24x2 = 52 + 96x + -52 + -96x

Combine like terms: 48x + -96x = -48x
-52 + -48x + -24x2 = 52 + 96x + -52 + -96x

Reorder the terms:
-52 + -48x + -24x2 = 52 + -52 + 96x + -96x

Combine like terms: 52 + -52 = 0
-52 + -48x + -24x2 = 0 + 96x + -96x
-52 + -48x + -24x2 = 96x + -96x

Combine like terms: 96x + -96x = 0
-52 + -48x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(13 + 12x + 6x2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(13 + 12x + 6x2)' equal to zero and attempt to solve:

Simplifying
13 + 12x + 6x2 = 0

Solving
13 + 12x + 6x2 = 0

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

Divide each side by '6'.
2.166666667 + 2x + x2 = 0

Move the constant term to the right:

Add '-2.166666667' to each side of the equation.
2.166666667 + 2x + -2.166666667 + x2 = 0 + -2.166666667

Reorder the terms:
2.166666667 + -2.166666667 + 2x + x2 = 0 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + -2.166666667
2x + x2 = 0 + -2.166666667

Combine like terms: 0 + -2.166666667 = -2.166666667
2x + x2 = -2.166666667

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 = -2.166666667 + 1

Reorder the terms:
1 + 2x + x2 = -2.166666667 + 1

Combine like terms: -2.166666667 + 1 = -1.166666667
1 + 2x + x2 = -1.166666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = -1.166666667

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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