a^2=a+42

Solution for a^2=a+42 equation:

Simplifying
a2 = a + 42

Reorder the terms:
a2 = 42 + a

Solving
a2 = 42 + a

Solving for variable 'a'.

Reorder the terms:
-42 + -1a + a2 = 42 + a + -42 + -1a

Reorder the terms:
-42 + -1a + a2 = 42 + -42 + a + -1a

Combine like terms: 42 + -42 = 0
-42 + -1a + a2 = 0 + a + -1a
-42 + -1a + a2 = a + -1a

Combine like terms: a + -1a = 0
-42 + -1a + a2 = 0

Factor a trinomial.
(-6 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
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
Solution
a = {-6, 7}