11a^2+12a-9=6a^2

Solution for 11a^2+12a-9=6a^2 equation:

Simplifying
11a2 + 12a + -9 = 6a2

Reorder the terms:
-9 + 12a + 11a2 = 6a2

Solving
-9 + 12a + 11a2 = 6a2

Solving for variable 'a'.

Combine like terms: 11a2 + -6a2 = 5a2
-9 + 12a + 5a2 = 6a2 + -6a2

Combine like terms: 6a2 + -6a2 = 0
-9 + 12a + 5a2 = 0

Factor a trinomial.
(-3 + -1a)(3 + -5a) = 0

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 '(3 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

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

Combine like terms: 3 + -3 = 0
0 + -5a = 0 + -3
-5a = 0 + -3

Combine like terms: 0 + -3 = -3
-5a = -3

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {-3, 0.6}