a^2=7a+8

Solution for a^2=7a+8 equation:

Simplifying
a2 = 7a + 8

Reorder the terms:
a2 = 8 + 7a

Solving
a2 = 8 + 7a

Solving for variable 'a'.

Reorder the terms:
-8 + -7a + a2 = 8 + 7a + -8 + -7a

Reorder the terms:
-8 + -7a + a2 = 8 + -8 + 7a + -7a

Combine like terms: 8 + -8 = 0
-8 + -7a + a2 = 0 + 7a + -7a
-8 + -7a + a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-8 + -7a + 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}