(-5y^2-8y-7)+(4y^2+9y-2)-(3y^2-8y-6)=

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Solution for (-5y^2-8y-7)+(4y^2+9y-2)-(3y^2-8y-6)= equation:


Simplifying
(-5y2 + -8y + -7) + (4y2 + 9y + -2) + -1(3y2 + -8y + -6) = 0

Reorder the terms:
(-7 + -8y + -5y2) + (4y2 + 9y + -2) + -1(3y2 + -8y + -6) = 0

Remove parenthesis around (-7 + -8y + -5y2)
-7 + -8y + -5y2 + (4y2 + 9y + -2) + -1(3y2 + -8y + -6) = 0

Reorder the terms:
-7 + -8y + -5y2 + (-2 + 9y + 4y2) + -1(3y2 + -8y + -6) = 0

Remove parenthesis around (-2 + 9y + 4y2)
-7 + -8y + -5y2 + -2 + 9y + 4y2 + -1(3y2 + -8y + -6) = 0

Reorder the terms:
-7 + -8y + -5y2 + -2 + 9y + 4y2 + -1(-6 + -8y + 3y2) = 0
-7 + -8y + -5y2 + -2 + 9y + 4y2 + (-6 * -1 + -8y * -1 + 3y2 * -1) = 0
-7 + -8y + -5y2 + -2 + 9y + 4y2 + (6 + 8y + -3y2) = 0

Reorder the terms:
-7 + -2 + 6 + -8y + 9y + 8y + -5y2 + 4y2 + -3y2 = 0

Combine like terms: -7 + -2 = -9
-9 + 6 + -8y + 9y + 8y + -5y2 + 4y2 + -3y2 = 0

Combine like terms: -9 + 6 = -3
-3 + -8y + 9y + 8y + -5y2 + 4y2 + -3y2 = 0

Combine like terms: -8y + 9y = 1y
-3 + 1y + 8y + -5y2 + 4y2 + -3y2 = 0

Combine like terms: 1y + 8y = 9y
-3 + 9y + -5y2 + 4y2 + -3y2 = 0

Combine like terms: -5y2 + 4y2 = -1y2
-3 + 9y + -1y2 + -3y2 = 0

Combine like terms: -1y2 + -3y2 = -4y2
-3 + 9y + -4y2 = 0

Solving
-3 + 9y + -4y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.75 + -2.25y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.25y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.25y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.25y + y2 = 0 + -0.75
-2.25y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.25y + y2 = -0.75

The y term is -2.25y.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25y + 1.265625 + y2 = -0.75 + 1.265625

Reorder the terms:
1.265625 + -2.25y + y2 = -0.75 + 1.265625

Combine like terms: -0.75 + 1.265625 = 0.515625
1.265625 + -2.25y + y2 = 0.515625

Factor a perfect square on the left side:
(y + -1.125)(y + -1.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(y + -1.125) equal to 0.718070331 and -0.718070331.

Subproblem 1

y + -1.125 = 0.718070331 Simplifying y + -1.125 = 0.718070331 Reorder the terms: -1.125 + y = 0.718070331 Solving -1.125 + y = 0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = 0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = 0.718070331 + 1.125 y = 0.718070331 + 1.125 Combine like terms: 0.718070331 + 1.125 = 1.843070331 y = 1.843070331 Simplifying y = 1.843070331

Subproblem 2

y + -1.125 = -0.718070331 Simplifying y + -1.125 = -0.718070331 Reorder the terms: -1.125 + y = -0.718070331 Solving -1.125 + y = -0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = -0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = -0.718070331 + 1.125 y = -0.718070331 + 1.125 Combine like terms: -0.718070331 + 1.125 = 0.406929669 y = 0.406929669 Simplifying y = 0.406929669

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.843070331, 0.406929669}

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