5a^2+a-6=0

Solution for 5a^2+a-6=0 equation:

Simplifying
5a2 + a + -6 = 0

Reorder the terms:
-6 + a + 5a2 = 0

Solving
-6 + a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -5a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -5a)' equal to zero and attempt to solve:

Simplifying
-6 + -5a = 0

Solving
-6 + -5a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5a = 0 + 6
-5a = 0 + 6

Combine like terms: 0 + 6 = 6
-5a = 6

Divide each side by '-5'.
a = -1.2

Simplifying
a = -1.2
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 = {-1.2, 1}