y(y-12)-16=0

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Solution for y(y-12)-16=0 equation:


Simplifying
y(y + -12) + -16 = 0

Reorder the terms:
y(-12 + y) + -16 = 0
(-12 * y + y * y) + -16 = 0
(-12y + y2) + -16 = 0

Reorder the terms:
-16 + -12y + y2 = 0

Solving
-16 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -12y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -12y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -12y + y2 = 0 + 16
-12y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-12y + y2 = 16

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 16 + 36

Reorder the terms:
36 + -12y + y2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + -12y + y2 = 52

Factor a perfect square on the left side:
(y + -6)(y + -6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(y + -6) equal to 7.211102551 and -7.211102551.

Subproblem 1

y + -6 = 7.211102551 Simplifying y + -6 = 7.211102551 Reorder the terms: -6 + y = 7.211102551 Solving -6 + y = 7.211102551 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + y = 7.211102551 + 6 y = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 y = 13.211102551 Simplifying y = 13.211102551

Subproblem 2

y + -6 = -7.211102551 Simplifying y + -6 = -7.211102551 Reorder the terms: -6 + y = -7.211102551 Solving -6 + y = -7.211102551 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + y = -7.211102551 + 6 y = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 y = -1.211102551 Simplifying y = -1.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.211102551, -1.211102551}

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