2a^2=-6+8a

Solution for 2a^2=-6+8a equation:

Simplifying
2a2 = -6 + 8a

Solving
2a2 = -6 + 8a

Solving for variable 'a'.

Reorder the terms:
6 + -8a + 2a2 = -6 + 8a + 6 + -8a

Reorder the terms:
6 + -8a + 2a2 = -6 + 6 + 8a + -8a

Combine like terms: -6 + 6 = 0
6 + -8a + 2a2 = 0 + 8a + -8a
6 + -8a + 2a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
6 + -8a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4a + a2) = 0

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

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

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

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

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