a^2-2a=(8a-8)-1

Solution for a^2-2a=(8a-8)-1 equation:

Simplifying
a2 + -2a = (8a + -8) + -1

Reorder the terms:
-2a + a2 = (8a + -8) + -1

Reorder the terms:
-2a + a2 = (-8 + 8a) + -1

Remove parenthesis around (-8 + 8a)
-2a + a2 = -8 + 8a + -1

Reorder the terms:
-2a + a2 = -8 + -1 + 8a

Combine like terms: -8 + -1 = -9
-2a + a2 = -9 + 8a

Solving
-2a + a2 = -9 + 8a

Solving for variable 'a'.

Reorder the terms:
9 + -2a + -8a + a2 = -9 + 8a + 9 + -8a

Combine like terms: -2a + -8a = -10a
9 + -10a + a2 = -9 + 8a + 9 + -8a

Reorder the terms:
9 + -10a + a2 = -9 + 9 + 8a + -8a

Combine like terms: -9 + 9 = 0
9 + -10a + a2 = 0 + 8a + -8a
9 + -10a + a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
9 + -10a + a2 = 0

Factor a trinomial.
(1 + -1a)(9 + -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 '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {1, 9}