3a^2-10a+3=-5

Solution for 3a^2-10a+3=-5 equation:

Simplifying
3a2 + -10a + 3 = -5

Reorder the terms:
3 + -10a + 3a2 = -5

Solving
3 + -10a + 3a2 = -5

Solving for variable 'a'.

Reorder the terms:
3 + 5 + -10a + 3a2 = -5 + 5

Combine like terms: 3 + 5 = 8
8 + -10a + 3a2 = -5 + 5

Combine like terms: -5 + 5 = 0
8 + -10a + 3a2 = 0

Factor a trinomial.
(4 + -3a)(2 + -1a) = 0

Subproblem 1
Set the factor '(4 + -3a)' equal to zero and attempt to solve:

Simplifying
4 + -3a = 0

Solving
4 + -3a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4

Combine like terms: 0 + -4 = -4
-3a = -4

Divide each side by '-3'.
a = 1.333333333

Simplifying
a = 1.333333333
Subproblem 2
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
Solution
a = {1.333333333, 2}