(3y^2+2y-3)-(-9y+6)=

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Solution for (3y^2+2y-3)-(-9y+6)= equation:


Simplifying
(3y2 + 2y + -3) + -1(-9y + 6) = 0

Reorder the terms:
(-3 + 2y + 3y2) + -1(-9y + 6) = 0

Remove parenthesis around (-3 + 2y + 3y2)
-3 + 2y + 3y2 + -1(-9y + 6) = 0

Reorder the terms:
-3 + 2y + 3y2 + -1(6 + -9y) = 0
-3 + 2y + 3y2 + (6 * -1 + -9y * -1) = 0
-3 + 2y + 3y2 + (-6 + 9y) = 0

Reorder the terms:
-3 + -6 + 2y + 9y + 3y2 = 0

Combine like terms: -3 + -6 = -9
-9 + 2y + 9y + 3y2 = 0

Combine like terms: 2y + 9y = 11y
-9 + 11y + 3y2 = 0

Solving
-9 + 11y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-3 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.666666667y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.666666667y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.666666667y + y2 = 0 + 3
3.666666667y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.666666667y + y2 = 3

The y term is 3.666666667y.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667y + 3.361111114 + y2 = 3 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = 3 + 3.361111114

Combine like terms: 3 + 3.361111114 = 6.361111114
3.361111114 + 3.666666667y + y2 = 6.361111114

Factor a perfect square on the left side:
(y + 1.833333334)(y + 1.833333334) = 6.361111114

Calculate the square root of the right side: 2.522124326

Break this problem into two subproblems by setting 
(y + 1.833333334) equal to 2.522124326 and -2.522124326.

Subproblem 1

y + 1.833333334 = 2.522124326 Simplifying y + 1.833333334 = 2.522124326 Reorder the terms: 1.833333334 + y = 2.522124326 Solving 1.833333334 + y = 2.522124326 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + y = 2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + y = 2.522124326 + -1.833333334 y = 2.522124326 + -1.833333334 Combine like terms: 2.522124326 + -1.833333334 = 0.688790992 y = 0.688790992 Simplifying y = 0.688790992

Subproblem 2

y + 1.833333334 = -2.522124326 Simplifying y + 1.833333334 = -2.522124326 Reorder the terms: 1.833333334 + y = -2.522124326 Solving 1.833333334 + y = -2.522124326 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + y = -2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + y = -2.522124326 + -1.833333334 y = -2.522124326 + -1.833333334 Combine like terms: -2.522124326 + -1.833333334 = -4.35545766 y = -4.35545766 Simplifying y = -4.35545766

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.688790992, -4.35545766}

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