2a^2=6-4a

Solution for 2a^2=6-4a equation:

Simplifying
2a2 = 6 + -4a

Solving
2a2 = 6 + -4a

Solving for variable 'a'.

Reorder the terms:
-6 + 4a + 2a2 = 6 + -4a + -6 + 4a

Reorder the terms:
-6 + 4a + 2a2 = 6 + -6 + -4a + 4a

Combine like terms: 6 + -6 = 0
-6 + 4a + 2a2 = 0 + -4a + 4a
-6 + 4a + 2a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
-6 + 4a + 2a2 = 0

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-3, 1}