3a^2=-a+2

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

Simplifying
3a2 = -1a + 2

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

Solving
3a2 = 2 + -1a

Solving for variable 'a'.

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

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

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

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

Factor a trinomial.
(-1 + -1a)(2 + -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 '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

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

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

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-1, 0.6666666667}