4a^2+6a=108

Solution for 4a^2+6a=108 equation:

Simplifying
4a2 + 6a = 108

Reorder the terms:
6a + 4a2 = 108

Solving
6a + 4a2 = 108

Solving for variable 'a'.

Reorder the terms:
-108 + 6a + 4a2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 6a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 3a + 2a2) = 0

Factor a trinomial.
2((-6 + -1a)(9 + -2a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 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 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve:

Simplifying
9 + -2a = 0

Solving
9 + -2a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2a = 0 + -9
-2a = 0 + -9

Combine like terms: 0 + -9 = -9
-2a = -9

Divide each side by '-2'.
a = 4.5

Simplifying
a = 4.5
Solution
a = {-6, 4.5}