6a^2+6a-30=6

Solution for 6a^2+6a-30=6 equation:

Simplifying
6a2 + 6a + -30 = 6

Reorder the terms:
-30 + 6a + 6a2 = 6

Solving
-30 + 6a + 6a2 = 6

Solving for variable 'a'.

Reorder the terms:
-30 + -6 + 6a + 6a2 = 6 + -6

Combine like terms: -30 + -6 = -36
-36 + 6a + 6a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-36 + 6a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + a + a2) = 0

Factor a trinomial.
6((-3 + -1a)(2 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
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 = {-3, 2}