3(y-3)2y-9+y=

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Solution for 3(y-3)2y-9+y= equation:


Simplifying
3(y + -3) * 2y + -9 + y = 0

Reorder the terms:
3(-3 + y) * 2y + -9 + y = 0

Reorder the terms for easier multiplication:
3 * 2y(-3 + y) + -9 + y = 0

Multiply 3 * 2
6y(-3 + y) + -9 + y = 0
(-3 * 6y + y * 6y) + -9 + y = 0
(-18y + 6y2) + -9 + y = 0

Reorder the terms:
-9 + -18y + y + 6y2 = 0

Combine like terms: -18y + y = -17y
-9 + -17y + 6y2 = 0

Solving
-9 + -17y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
-1.5 + -2.833333333y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.833333333y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.833333333y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.833333333y + y2 = 0 + 1.5
-2.833333333y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2.833333333y + y2 = 1.5

The y term is -2.833333333y.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333y + 2.006944445 + y2 = 1.5 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333y + y2 = 1.5 + 2.006944445

Combine like terms: 1.5 + 2.006944445 = 3.506944445
2.006944445 + -2.833333333y + y2 = 3.506944445

Factor a perfect square on the left side:
(y + -1.416666667)(y + -1.416666667) = 3.506944445

Calculate the square root of the right side: 1.872683755

Break this problem into two subproblems by setting 
(y + -1.416666667) equal to 1.872683755 and -1.872683755.

Subproblem 1

y + -1.416666667 = 1.872683755 Simplifying y + -1.416666667 = 1.872683755 Reorder the terms: -1.416666667 + y = 1.872683755 Solving -1.416666667 + y = 1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + y = 1.872683755 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + y = 1.872683755 + 1.416666667 y = 1.872683755 + 1.416666667 Combine like terms: 1.872683755 + 1.416666667 = 3.289350422 y = 3.289350422 Simplifying y = 3.289350422

Subproblem 2

y + -1.416666667 = -1.872683755 Simplifying y + -1.416666667 = -1.872683755 Reorder the terms: -1.416666667 + y = -1.872683755 Solving -1.416666667 + y = -1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + y = -1.872683755 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + y = -1.872683755 + 1.416666667 y = -1.872683755 + 1.416666667 Combine like terms: -1.872683755 + 1.416666667 = -0.456017088 y = -0.456017088 Simplifying y = -0.456017088

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.289350422, -0.456017088}

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