30=w(w+3)

Solution for 30=w(w+3) equation:

Simplifying
30 = w(w + 3)

Reorder the terms:
30 = w(3 + w)
30 = (3 * w + w * w)
30 = (3w + w2)

Solving
30 = 3w + w2

Solving for variable 'w'.

Reorder the terms:
30 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
30 + -3w + -1w2 = 0 + w2 + -1w2
30 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
30 + -3w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + 3w + w2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3w + 30 + w2 = 0 + 30

Reorder the terms:
-30 + 30 + 3w + w2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3w + w2 = 0 + 30
3w + w2 = 0 + 30

Combine like terms: 0 + 30 = 30
3w + w2 = 30

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 30 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3w + w2 = 32.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(w + 1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
w + 1.5 = 5.678908346

Simplifying
w + 1.5 = 5.678908346

Reorder the terms:
1.5 + w = 5.678908346

Solving
1.5 + w = 5.678908346

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 5.678908346 + -1.5
w = 5.678908346 + -1.5

Combine like terms: 5.678908346 + -1.5 = 4.178908346
w = 4.178908346

Simplifying
w = 4.178908346

Subproblem 2
w + 1.5 = -5.678908346

Simplifying
w + 1.5 = -5.678908346

Reorder the terms:
1.5 + w = -5.678908346

Solving
1.5 + w = -5.678908346

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -5.678908346 + -1.5
w = -5.678908346 + -1.5

Combine like terms: -5.678908346 + -1.5 = -7.178908346
w = -7.178908346

Simplifying
w = -7.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.178908346, -7.178908346}