27-(36-y)y=12

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Solution for 27-(36-y)y=12 equation:


Simplifying
27 + -1(36 + -1y) * y = 12

Reorder the terms for easier multiplication:
27 + -1y(36 + -1y) = 12
27 + (36 * -1y + -1y * -1y) = 12
27 + (-36y + 1y2) = 12

Solving
27 + -36y + 1y2 = 12

Solving for variable 'y'.

Reorder the terms:
27 + -12 + -36y + 1y2 = 12 + -12

Combine like terms: 27 + -12 = 15
15 + -36y + 1y2 = 12 + -12

Combine like terms: 12 + -12 = 0
15 + -36y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -36y + -15 + y2 = 0 + -15

Reorder the terms:
15 + -15 + -36y + y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -36y + y2 = 0 + -15
-36y + y2 = 0 + -15

Combine like terms: 0 + -15 = -15
-36y + y2 = -15

The y term is -36y.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36y + 324 + y2 = -15 + 324

Reorder the terms:
324 + -36y + y2 = -15 + 324

Combine like terms: -15 + 324 = 309
324 + -36y + y2 = 309

Factor a perfect square on the left side:
(y + -18)(y + -18) = 309

Calculate the square root of the right side: 17.578395831

Break this problem into two subproblems by setting 
(y + -18) equal to 17.578395831 and -17.578395831.

Subproblem 1

y + -18 = 17.578395831 Simplifying y + -18 = 17.578395831 Reorder the terms: -18 + y = 17.578395831 Solving -18 + y = 17.578395831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = 17.578395831 + 18 Combine like terms: -18 + 18 = 0 0 + y = 17.578395831 + 18 y = 17.578395831 + 18 Combine like terms: 17.578395831 + 18 = 35.578395831 y = 35.578395831 Simplifying y = 35.578395831

Subproblem 2

y + -18 = -17.578395831 Simplifying y + -18 = -17.578395831 Reorder the terms: -18 + y = -17.578395831 Solving -18 + y = -17.578395831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = -17.578395831 + 18 Combine like terms: -18 + 18 = 0 0 + y = -17.578395831 + 18 y = -17.578395831 + 18 Combine like terms: -17.578395831 + 18 = 0.421604169 y = 0.421604169 Simplifying y = 0.421604169

Solution

The solution to the problem is based on the solutions from the subproblems. y = {35.578395831, 0.421604169}

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