3a^2+1=2-2a

Solution for 3a^2+1=2-2a equation:

Simplifying
3a2 + 1 = 2 + -2a

Reorder the terms:
1 + 3a2 = 2 + -2a

Solving
1 + 3a2 = 2 + -2a

Solving for variable 'a'.

Reorder the terms:
1 + -2 + 2a + 3a2 = 2 + -2a + -2 + 2a

Combine like terms: 1 + -2 = -1
-1 + 2a + 3a2 = 2 + -2a + -2 + 2a

Reorder the terms:
-1 + 2a + 3a2 = 2 + -2 + -2a + 2a

Combine like terms: 2 + -2 = 0
-1 + 2a + 3a2 = 0 + -2a + 2a
-1 + 2a + 3a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
-1 + 2a + 3a2 = 0

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

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 '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

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

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-1, 0.3333333333}