5a^2+10a-6a-12=0

Solution for 5a^2+10a-6a-12=0 equation:

Simplifying
5a2 + 10a + -6a + -12 = 0

Reorder the terms:
-12 + 10a + -6a + 5a2 = 0

Combine like terms: 10a + -6a = 4a
-12 + 4a + 5a2 = 0

Solving
-12 + 4a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1a)(6 + -5a) = 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 '(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
Solution
a = {-2, 1.2}