5a(a+1)=30

Solution for 5a(a+1)=30 equation:

Simplifying
5a(a + 1) = 30

Reorder the terms:
5a(1 + a) = 30
(1 * 5a + a * 5a) = 30
(5a + 5a2) = 30

Solving
5a + 5a2 = 30

Solving for variable 'a'.

Reorder the terms:
-30 + 5a + 5a2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 5a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + a + a2) = 0

Factor a trinomial.
5((-3 + -1a)(2 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-3, 2}