12y+y(y-6)=4

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Solution for 12y+y(y-6)=4 equation:


Simplifying
12y + y(y + -6) = 4

Reorder the terms:
12y + y(-6 + y) = 4
12y + (-6 * y + y * y) = 4
12y + (-6y + y2) = 4

Combine like terms: 12y + -6y = 6y
6y + y2 = 4

Solving
6y + y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 6y + y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 6y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6y + y2 = 0 + 4
6y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
6y + y2 = 4

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 4 + 9

Reorder the terms:
9 + 6y + y2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6y + y2 = 13

Factor a perfect square on the left side:
(y + 3)(y + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1

y + 3 = 3.605551275 Simplifying y + 3 = 3.605551275 Reorder the terms: 3 + y = 3.605551275 Solving 3 + y = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.605551275 + -3 y = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 y = 0.605551275 Simplifying y = 0.605551275

Subproblem 2

y + 3 = -3.605551275 Simplifying y + 3 = -3.605551275 Reorder the terms: 3 + y = -3.605551275 Solving 3 + y = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.605551275 + -3 y = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 y = -6.605551275 Simplifying y = -6.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.605551275, -6.605551275}

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