a^2+a-9=-3+6a

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

Simplifying
a2 + a + -9 = -3 + 6a

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

Solving
-9 + a + a2 = -3 + 6a

Solving for variable 'a'.

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

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

Combine like terms: a + -6a = -5a
-6 + -5a + a2 = -3 + 6a + 3 + -6a

Reorder the terms:
-6 + -5a + a2 = -3 + 3 + 6a + -6a

Combine like terms: -3 + 3 = 0
-6 + -5a + a2 = 0 + 6a + -6a
-6 + -5a + a2 = 6a + -6a

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

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

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 '(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
Solution
a = {-1, 6}