3a^2=-5a+2

Solution for 3a^2=-5a+2 equation:

Simplifying
3a2 = -5a + 2

Reorder the terms:
3a2 = 2 + -5a

Solving
3a2 = 2 + -5a

Solving for variable 'a'.

Reorder the terms:
-2 + 5a + 3a2 = 2 + -5a + -2 + 5a

Reorder the terms:
-2 + 5a + 3a2 = 2 + -2 + -5a + 5a

Combine like terms: 2 + -2 = 0
-2 + 5a + 3a2 = 0 + -5a + 5a
-2 + 5a + 3a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
-2 + 5a + 3a2 = 0

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

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

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 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 + -1a = 0 + 2

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2
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 = {-2, 0.3333333333}