9a^2=-6+15a

Solution for 9a^2=-6+15a equation:

Simplifying
9a2 = -6 + 15a

Solving
9a2 = -6 + 15a

Solving for variable 'a'.

Reorder the terms:
6 + -15a + 9a2 = -6 + 15a + 6 + -15a

Reorder the terms:
6 + -15a + 9a2 = -6 + 6 + 15a + -15a

Combine like terms: -6 + 6 = 0
6 + -15a + 9a2 = 0 + 15a + -15a
6 + -15a + 9a2 = 15a + -15a

Combine like terms: 15a + -15a = 0
6 + -15a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -5a + 3a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 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 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {0.6666666667, 1}