9a^2-15a-22=5+3a

Solution for 9a^2-15a-22=5+3a equation:

Simplifying
9a2 + -15a + -22 = 5 + 3a

Reorder the terms:
-22 + -15a + 9a2 = 5 + 3a

Solving
-22 + -15a + 9a2 = 5 + 3a

Solving for variable 'a'.

Reorder the terms:
-22 + -5 + -15a + -3a + 9a2 = 5 + 3a + -5 + -3a

Combine like terms: -22 + -5 = -27
-27 + -15a + -3a + 9a2 = 5 + 3a + -5 + -3a

Combine like terms: -15a + -3a = -18a
-27 + -18a + 9a2 = 5 + 3a + -5 + -3a

Reorder the terms:
-27 + -18a + 9a2 = 5 + -5 + 3a + -3a

Combine like terms: 5 + -5 = 0
-27 + -18a + 9a2 = 0 + 3a + -3a
-27 + -18a + 9a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-27 + -18a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + -2a + a2) = 0

Factor a trinomial.
9((-1 + -1a)(3 + -1a)) = 0

Ignore the factor 9.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-1, 3}