30=a(a+1)

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

Simplifying
30 = a(a + 1)

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

Solving
30 = 1a + a2

Solving for variable 'a'.

Reorder the terms:
30 + -1a + -1a2 = 1a + -1a + a2 + -1a2

Combine like terms: 1a + -1a = 0
30 + -1a + -1a2 = 0 + a2 + -1a2
30 + -1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
30 + -1a + -1a2 = 0

Factor a trinomial.
(5 + -1a)(6 + a) = 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 '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 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 + a = 0 + -6

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

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

Simplifying
a = -6
Solution
a = {5, -6}