3a^2+3a=60

Solution for 3a^2+3a=60 equation:

Simplifying
3a2 + 3a = 60

Reorder the terms:
3a + 3a2 = 60

Solving
3a + 3a2 = 60

Solving for variable 'a'.

Reorder the terms:
-60 + 3a + 3a2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 3a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + a + a2) = 0

Factor a trinomial.
3((-5 + -1a)(4 + -1a)) = 0

Ignore the factor 3.
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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-5, 4}