5a^2-3a-2=0

Solution for 5a^2-3a-2=0 equation:

Simplifying
5a2 + -3a + -2 = 0

Reorder the terms:
-2 + -3a + 5a2 = 0

Solving
-2 + -3a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -5a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve:

Simplifying
-2 + -5a = 0

Solving
-2 + -5a = 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 + -5a = 0 + 2

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

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

Divide each side by '-5'.
a = -0.4

Simplifying
a = -0.4
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 = {-0.4, 1}