(2y^2-9y+16)-(5y^2+3y-3)=

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Solution for (2y^2-9y+16)-(5y^2+3y-3)= equation: 


Simplifying
(2y2 + -9y + 16) + -1(5y2 + 3y + -3) = 0

Reorder the terms:
(16 + -9y + 2y2) + -1(5y2 + 3y + -3) = 0

Remove parenthesis around (16 + -9y + 2y2)
16 + -9y + 2y2 + -1(5y2 + 3y + -3) = 0

Reorder the terms:
16 + -9y + 2y2 + -1(-3 + 3y + 5y2) = 0
16 + -9y + 2y2 + (-3 * -1 + 3y * -1 + 5y2 * -1) = 0
16 + -9y + 2y2 + (3 + -3y + -5y2) = 0

Reorder the terms:
16 + 3 + -9y + -3y + 2y2 + -5y2 = 0

Combine like terms: 16 + 3 = 19
19 + -9y + -3y + 2y2 + -5y2 = 0

Combine like terms: -9y + -3y = -12y
19 + -12y + 2y2 + -5y2 = 0

Combine like terms: 2y2 + -5y2 = -3y2
19 + -12y + -3y2 = 0

Solving
19 + -12y + -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'.
-6.333333333 + 4y + y2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 4y + 6.333333333 + y2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 4y + y2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 4y + y2 = 0 + 6.333333333
4y + y2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
4y + y2 = 6.333333333

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 6.333333333 + 4

Reorder the terms:
4 + 4y + y2 = 6.333333333 + 4

Combine like terms: 6.333333333 + 4 = 10.333333333
4 + 4y + y2 = 10.333333333

Factor a perfect square on the left side:
(y + 2)(y + 2) = 10.333333333

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(y + 2) equal to 3.214550254 and -3.214550254.


Subproblem 1
y + 2 = 3.214550254

Simplifying
y + 2 = 3.214550254

Reorder the terms:
2 + y = 3.214550254

Solving
2 + y = 3.214550254

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = 3.214550254 + -2

Combine like terms: 2 + -2 = 0
0 + y = 3.214550254 + -2
y = 3.214550254 + -2

Combine like terms: 3.214550254 + -2 = 1.214550254
y = 1.214550254

Simplifying
y = 1.214550254


Subproblem 2
y + 2 = -3.214550254

Simplifying
y + 2 = -3.214550254

Reorder the terms:
2 + y = -3.214550254

Solving
2 + y = -3.214550254

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = -3.214550254 + -2

Combine like terms: 2 + -2 = 0
0 + y = -3.214550254 + -2
y = -3.214550254 + -2

Combine like terms: -3.214550254 + -2 = -5.214550254
y = -5.214550254

Simplifying
y = -5.214550254


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.214550254, -5.214550254}

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