(30+2y)(y)=100

Solution for (30+2y)(y)=100 equation:

Simplifying
(30 + 2y)(y) = 100

Reorder the terms for easier multiplication:
y(30 + 2y) = 100
(30 * y + 2y * y) = 100
(30y + 2y2) = 100

Solving
30y + 2y2 = 100

Solving for variable 'y'.

Reorder the terms:
-100 + 30y + 2y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 30y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 15y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 15y + y2)' equal to zero and attempt to solve:

Simplifying
-50 + 15y + y2 = 0

Solving
-50 + 15y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 15y + 50 + y2 = 0 + 50

Reorder the terms:
-50 + 50 + 15y + y2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 15y + y2 = 0 + 50
15y + y2 = 0 + 50

Combine like terms: 0 + 50 = 50
15y + y2 = 50

The y term is 15y.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15y + 56.25 + y2 = 50 + 56.25

Reorder the terms:
56.25 + 15y + y2 = 50 + 56.25

Combine like terms: 50 + 56.25 = 106.25
56.25 + 15y + y2 = 106.25

Factor a perfect square on the left side:
(y + 7.5)(y + 7.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(y + 7.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
y + 7.5 = 10.307764064

Simplifying
y + 7.5 = 10.307764064

Reorder the terms:
7.5 + y = 10.307764064

Solving
7.5 + y = 10.307764064

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = 10.307764064 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = 10.307764064 + -7.5
y = 10.307764064 + -7.5

Combine like terms: 10.307764064 + -7.5 = 2.807764064
y = 2.807764064

Simplifying
y = 2.807764064

Subproblem 2
y + 7.5 = -10.307764064

Simplifying
y + 7.5 = -10.307764064

Reorder the terms:
7.5 + y = -10.307764064

Solving
7.5 + y = -10.307764064

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = -10.307764064 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = -10.307764064 + -7.5
y = -10.307764064 + -7.5

Combine like terms: -10.307764064 + -7.5 = -17.807764064
y = -17.807764064

Simplifying
y = -17.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.807764064, -17.807764064}
Solution
y = {2.807764064, -17.807764064}