6x(2x+8)=8x-36

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Solution for 6x(2x+8)=8x-36 equation: 


Simplifying
6x(2x + 8) = 8x + -36

Reorder the terms:
6x(8 + 2x) = 8x + -36
(8 * 6x + 2x * 6x) = 8x + -36
(48x + 12x2) = 8x + -36

Reorder the terms:
48x + 12x2 = -36 + 8x

Solving
48x + 12x2 = -36 + 8x

Solving for variable 'x'.

Reorder the terms:
36 + 48x + -8x + 12x2 = -36 + 8x + 36 + -8x

Combine like terms: 48x + -8x = 40x
36 + 40x + 12x2 = -36 + 8x + 36 + -8x

Reorder the terms:
36 + 40x + 12x2 = -36 + 36 + 8x + -8x

Combine like terms: -36 + 36 = 0
36 + 40x + 12x2 = 0 + 8x + -8x
36 + 40x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
36 + 40x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 10x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + 10x + 3x2)' equal to zero and attempt to solve:

Simplifying
9 + 10x + 3x2 = 0

Solving
9 + 10x + 3x2 = 0

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

Divide each side by '3'.
3 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3.333333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 3.333333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3.333333333x + x2 = 0 + -3
3.333333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
3.333333333x + x2 = -3

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -3 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -3 + 2.777777779

Combine like terms: -3 + 2.777777779 = -0.222222221
2.777777779 + 3.333333333x + x2 = -0.222222221

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = -0.222222221

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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