a^2=-8+9a

Solution for a^2=-8+9a equation:

Simplifying
a2 = -8 + 9a

Solving
a2 = -8 + 9a

Solving for variable 'a'.

Reorder the terms:
8 + -9a + a2 = -8 + 9a + 8 + -9a

Reorder the terms:
8 + -9a + a2 = -8 + 8 + 9a + -9a

Combine like terms: -8 + 8 = 0
8 + -9a + a2 = 0 + 9a + -9a
8 + -9a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
8 + -9a + a2 = 0

Factor a trinomial.
(1 + -1a)(8 + -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 '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {1, 8}