a^2=7a+60

Solution for a^2=7a+60 equation:

Simplifying
a2 = 7a + 60

Reorder the terms:
a2 = 60 + 7a

Solving
a2 = 60 + 7a

Solving for variable 'a'.

Reorder the terms:
-60 + -7a + a2 = 60 + 7a + -60 + -7a

Reorder the terms:
-60 + -7a + a2 = 60 + -60 + 7a + -7a

Combine like terms: 60 + -60 = 0
-60 + -7a + a2 = 0 + 7a + -7a
-60 + -7a + a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-60 + -7a + a2 = 0

Factor a trinomial.
(-5 + -1a)(12 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-5, 12}