6x^2+8=4(3x-20)

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Solution for 6x^2+8=4(3x-20) equation: 


Simplifying
6x2 + 8 = 4(3x + -20)

Reorder the terms:
8 + 6x2 = 4(3x + -20)

Reorder the terms:
8 + 6x2 = 4(-20 + 3x)
8 + 6x2 = (-20 * 4 + 3x * 4)
8 + 6x2 = (-80 + 12x)

Solving
8 + 6x2 = -80 + 12x

Solving for variable 'x'.

Reorder the terms:
8 + 80 + -12x + 6x2 = -80 + 12x + 80 + -12x

Combine like terms: 8 + 80 = 88
88 + -12x + 6x2 = -80 + 12x + 80 + -12x

Reorder the terms:
88 + -12x + 6x2 = -80 + 80 + 12x + -12x

Combine like terms: -80 + 80 = 0
88 + -12x + 6x2 = 0 + 12x + -12x
88 + -12x + 6x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
88 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(44 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(44 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
44 + -6x + 3x2 = 0

Solving
44 + -6x + 3x2 = 0

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

Divide each side by '3'.
14.66666667 + -2x + x2 = 0

Move the constant term to the right:

Add '-14.66666667' to each side of the equation.
14.66666667 + -2x + -14.66666667 + x2 = 0 + -14.66666667

Reorder the terms:
14.66666667 + -14.66666667 + -2x + x2 = 0 + -14.66666667

Combine like terms: 14.66666667 + -14.66666667 = 0.00000000
0.00000000 + -2x + x2 = 0 + -14.66666667
-2x + x2 = 0 + -14.66666667

Combine like terms: 0 + -14.66666667 = -14.66666667
-2x + x2 = -14.66666667

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 = -14.66666667 + 1

Reorder the terms:
1 + -2x + x2 = -14.66666667 + 1

Combine like terms: -14.66666667 + 1 = -13.66666667
1 + -2x + x2 = -13.66666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = -13.66666667

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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