154=n(n+3)

Solution for 154=n(n+3) equation:

Simplifying
154 = n(n + 3)

Reorder the terms:
154 = n(3 + n)
154 = (3 * n + n * n)
154 = (3n + n2)

Solving
154 = 3n + n2

Solving for variable 'n'.

Reorder the terms:
154 + -3n + -1n2 = 3n + -3n + n2 + -1n2

Combine like terms: 3n + -3n = 0
154 + -3n + -1n2 = 0 + n2 + -1n2
154 + -3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
154 + -3n + -1n2 = 0

Factor a trinomial.
(11 + -1n)(14 + n) = 0

Subproblem 1
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Subproblem 2
Set the factor '(14 + n)' equal to zero and attempt to solve:

Simplifying
14 + n = 0

Solving
14 + n = 0

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

Add '-14' to each side of the equation.
14 + -14 + n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + n = 0 + -14
n = 0 + -14

Combine like terms: 0 + -14 = -14
n = -14

Simplifying
n = -14
Solution
n = {11, -14}