4n+30=n(4n+30)

Solution for 4n+30=n(4n+30) equation:

Simplifying
4n + 30 = n(4n + 30)

Reorder the terms:
30 + 4n = n(4n + 30)

Reorder the terms:
30 + 4n = n(30 + 4n)
30 + 4n = (30 * n + 4n * n)
30 + 4n = (30n + 4n2)

Solving
30 + 4n = 30n + 4n2

Solving for variable 'n'.

Combine like terms: 4n + -30n = -26n
30 + -26n + -4n2 = 30n + 4n2 + -30n + -4n2

Reorder the terms:
30 + -26n + -4n2 = 30n + -30n + 4n2 + -4n2

Combine like terms: 30n + -30n = 0
30 + -26n + -4n2 = 0 + 4n2 + -4n2
30 + -26n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
30 + -26n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -13n + -2n2) = 0

Factor a trinomial.
2((1 + -1n)(15 + 2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Subproblem 2
Set the factor '(15 + 2n)' equal to zero and attempt to solve:

Simplifying
15 + 2n = 0

Solving
15 + 2n = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2n = 0 + -15
2n = 0 + -15

Combine like terms: 0 + -15 = -15
2n = -15

Divide each side by '2'.
n = -7.5

Simplifying
n = -7.5
Solution
n = {1, -7.5}