2a^2x^2-8ax=-6

Solution for 2a^2x^2-8ax=-6 equation:

Simplifying
2a2x2 + -8ax = -6

Reorder the terms:
-8ax + 2a2x2 = -6

Solving
-8ax + 2a2x2 = -6

Solving for variable 'a'.

Reorder the terms:
6 + -8ax + 2a2x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -8ax + 2a2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4ax + a2x2) = 0

Factor a trinomial.
2((1 + -1ax)(3 + -1ax)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1ax)' equal to zero and attempt to solve:

Simplifying
1 + -1ax = 0

Solving
1 + -1ax = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1ax = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1ax = 0 + -1
-1ax = 0 + -1

Combine like terms: 0 + -1 = -1
-1ax = -1

Divide each side by '-1x'.
a = x-1

Simplifying
a = x-1
Subproblem 2
Set the factor '(3 + -1ax)' equal to zero and attempt to solve:

Simplifying
3 + -1ax = 0

Solving
3 + -1ax = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1ax = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1ax = 0 + -3
-1ax = 0 + -3

Combine like terms: 0 + -3 = -3
-1ax = -3

Divide each side by '-1x'.
a = 3x-1

Simplifying
a = 3x-1
Solution
a = {x-1, 3x-1}