6x^2+(12-8a)x-16a=0

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Solution for 6x^2+(12-8a)x-16a=0 equation: 


Simplifying
6x2 + (12 + -8a) * x + -16a = 0

Reorder the terms for easier multiplication:
6x2 + x(12 + -8a) + -16a = 0
6x2 + (12 * x + -8a * x) + -16a = 0

Reorder the terms:
6x2 + (-8ax + 12x) + -16a = 0
6x2 + (-8ax + 12x) + -16a = 0

Reorder the terms:
-16a + -8ax + 12x + 6x2 = 0

Solving
-16a + -8ax + 12x + 6x2 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-12x' to each side of the equation.
-16a + -8ax + 12x + -12x + 6x2 = 0 + -12x

Combine like terms: 12x + -12x = 0
-16a + -8ax + 0 + 6x2 = 0 + -12x
-16a + -8ax + 6x2 = 0 + -12x
Remove the zero:
-16a + -8ax + 6x2 = -12x

Add '-6x2' to each side of the equation.
-16a + -8ax + 6x2 + -6x2 = -12x + -6x2

Combine like terms: 6x2 + -6x2 = 0
-16a + -8ax + 0 = -12x + -6x2
-16a + -8ax = -12x + -6x2

Reorder the terms:
-16a + -8ax + 12x + 6x2 = -12x + 12x + -6x2 + 6x2

Combine like terms: -12x + 12x = 0
-16a + -8ax + 12x + 6x2 = 0 + -6x2 + 6x2
-16a + -8ax + 12x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-16a + -8ax + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8a + -4ax + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8a + -4ax + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-8a + -4ax + 6x + 3x2 = 0

Solving
-8a + -4ax + 6x + 3x2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '-6x' to each side of the equation.
-8a + -4ax + 6x + -6x + 3x2 = 0 + -6x

Combine like terms: 6x + -6x = 0
-8a + -4ax + 0 + 3x2 = 0 + -6x
-8a + -4ax + 3x2 = 0 + -6x
Remove the zero:
-8a + -4ax + 3x2 = -6x

Add '-3x2' to each side of the equation.
-8a + -4ax + 3x2 + -3x2 = -6x + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8a + -4ax + 0 = -6x + -3x2
-8a + -4ax = -6x + -3x2

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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