a^2=a+56

Solution for a^2=a+56 equation:

Simplifying
a2 = a + 56

Reorder the terms:
a2 = 56 + a

Solving
a2 = 56 + a

Solving for variable 'a'.

Reorder the terms:
-56 + -1a + a2 = 56 + a + -56 + -1a

Reorder the terms:
-56 + -1a + a2 = 56 + -56 + a + -1a

Combine like terms: 56 + -56 = 0
-56 + -1a + a2 = 0 + a + -1a
-56 + -1a + a2 = a + -1a

Combine like terms: a + -1a = 0
-56 + -1a + a2 = 0

Factor a trinomial.
(-7 + -1a)(8 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
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 = {-7, 8}