y^2-15y+42=0

Solution for y^2-15y+42=0 equation:

Simplifying
y2 + -15y + 42 = 0

Reorder the terms:
42 + -15y + y2 = 0

Solving
42 + -15y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -15y + -42 + y2 = 0 + -42

Reorder the terms:
42 + -42 + -15y + y2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -15y + y2 = 0 + -42
-15y + y2 = 0 + -42

Combine like terms: 0 + -42 = -42
-15y + y2 = -42

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 = -42 + 56.25

Reorder the terms:
56.25 + -15y + y2 = -42 + 56.25

Combine like terms: -42 + 56.25 = 14.25
56.25 + -15y + y2 = 14.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + -7.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
y + -7.5 = 3.774917218

Simplifying
y + -7.5 = 3.774917218

Reorder the terms:
-7.5 + y = 3.774917218

Solving
-7.5 + y = 3.774917218

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 = 3.774917218 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = 3.774917218 + 7.5
y = 3.774917218 + 7.5

Combine like terms: 3.774917218 + 7.5 = 11.274917218
y = 11.274917218

Simplifying
y = 11.274917218

Subproblem 2
y + -7.5 = -3.774917218

Simplifying
y + -7.5 = -3.774917218

Reorder the terms:
-7.5 + y = -3.774917218

Solving
-7.5 + y = -3.774917218

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 = -3.774917218 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = -3.774917218 + 7.5
y = -3.774917218 + 7.5

Combine like terms: -3.774917218 + 7.5 = 3.725082782
y = 3.725082782

Simplifying
y = 3.725082782

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.274917218, 3.725082782}