12y+5y(y-6)=4

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Solution for 12y+5y(y-6)=4 equation:


Simplifying
12y + 5y(y + -6) = 4

Reorder the terms:
12y + 5y(-6 + y) = 4
12y + (-6 * 5y + y * 5y) = 4
12y + (-30y + 5y2) = 4

Combine like terms: 12y + -30y = -18y
-18y + 5y2 = 4

Solving
-18y + 5y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + -18y + 5y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -18y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.8 + -3.6y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -3.6y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -3.6y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -3.6y + y2 = 0 + 0.8
-3.6y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-3.6y + y2 = 0.8

The y term is -3.6y.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6y + 3.24 + y2 = 0.8 + 3.24

Reorder the terms:
3.24 + -3.6y + y2 = 0.8 + 3.24

Combine like terms: 0.8 + 3.24 = 4.04
3.24 + -3.6y + y2 = 4.04

Factor a perfect square on the left side:
(y + -1.8)(y + -1.8) = 4.04

Calculate the square root of the right side: 2.009975124

Break this problem into two subproblems by setting 
(y + -1.8) equal to 2.009975124 and -2.009975124.

Subproblem 1

y + -1.8 = 2.009975124 Simplifying y + -1.8 = 2.009975124 Reorder the terms: -1.8 + y = 2.009975124 Solving -1.8 + y = 2.009975124 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = 2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 2.009975124 + 1.8 y = 2.009975124 + 1.8 Combine like terms: 2.009975124 + 1.8 = 3.809975124 y = 3.809975124 Simplifying y = 3.809975124

Subproblem 2

y + -1.8 = -2.009975124 Simplifying y + -1.8 = -2.009975124 Reorder the terms: -1.8 + y = -2.009975124 Solving -1.8 + y = -2.009975124 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = -2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -2.009975124 + 1.8 y = -2.009975124 + 1.8 Combine like terms: -2.009975124 + 1.8 = -0.209975124 y = -0.209975124 Simplifying y = -0.209975124

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.809975124, -0.209975124}

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