6a^2=-9a-3

Solution for 6a^2=-9a-3 equation:

Simplifying
6a2 = -9a + -3

Reorder the terms:
6a2 = -3 + -9a

Solving
6a2 = -3 + -9a

Solving for variable 'a'.

Reorder the terms:
3 + 9a + 6a2 = -3 + -9a + 3 + 9a

Reorder the terms:
3 + 9a + 6a2 = -3 + 3 + -9a + 9a

Combine like terms: -3 + 3 = 0
3 + 9a + 6a2 = 0 + -9a + 9a
3 + 9a + 6a2 = -9a + 9a

Combine like terms: -9a + 9a = 0
3 + 9a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3a + 2a2) = 0

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

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

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-1, -0.5}