a^2+a=64a+64

Solution for a^2+a=64a+64 equation:

Simplifying
a2 + a = 64a + 64

Reorder the terms:
a + a2 = 64a + 64

Reorder the terms:
a + a2 = 64 + 64a

Solving
a + a2 = 64 + 64a

Solving for variable 'a'.

Reorder the terms:
-64 + a + -64a + a2 = 64 + 64a + -64 + -64a

Combine like terms: a + -64a = -63a
-64 + -63a + a2 = 64 + 64a + -64 + -64a

Reorder the terms:
-64 + -63a + a2 = 64 + -64 + 64a + -64a

Combine like terms: 64 + -64 = 0
-64 + -63a + a2 = 0 + 64a + -64a
-64 + -63a + a2 = 64a + -64a

Combine like terms: 64a + -64a = 0
-64 + -63a + a2 = 0

Factor a trinomial.
(-1 + -1a)(64 + -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 '(64 + -1a)' equal to zero and attempt to solve:

Simplifying
64 + -1a = 0

Solving
64 + -1a = 0

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

Add '-64' to each side of the equation.
64 + -64 + -1a = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -1a = 0 + -64
-1a = 0 + -64

Combine like terms: 0 + -64 = -64
-1a = -64

Divide each side by '-1'.
a = 64

Simplifying
a = 64
Solution
a = {-1, 64}