(8y^2+19y-6)-(12y^2-12y-4)=

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Solution for (8y^2+19y-6)-(12y^2-12y-4)= equation:


Simplifying
(8y2 + 19y + -6) + -1(12y2 + -12y + -4) = 0

Reorder the terms:
(-6 + 19y + 8y2) + -1(12y2 + -12y + -4) = 0

Remove parenthesis around (-6 + 19y + 8y2)
-6 + 19y + 8y2 + -1(12y2 + -12y + -4) = 0

Reorder the terms:
-6 + 19y + 8y2 + -1(-4 + -12y + 12y2) = 0
-6 + 19y + 8y2 + (-4 * -1 + -12y * -1 + 12y2 * -1) = 0
-6 + 19y + 8y2 + (4 + 12y + -12y2) = 0

Reorder the terms:
-6 + 4 + 19y + 12y + 8y2 + -12y2 = 0

Combine like terms: -6 + 4 = -2
-2 + 19y + 12y + 8y2 + -12y2 = 0

Combine like terms: 19y + 12y = 31y
-2 + 31y + 8y2 + -12y2 = 0

Combine like terms: 8y2 + -12y2 = -4y2
-2 + 31y + -4y2 = 0

Solving
-2 + 31y + -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'.
0.5 + -7.75y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -7.75y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -7.75y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -7.75y + y2 = 0 + -0.5
-7.75y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-7.75y + y2 = -0.5

The y term is -7.75y.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75y + 15.015625 + y2 = -0.5 + 15.015625

Reorder the terms:
15.015625 + -7.75y + y2 = -0.5 + 15.015625

Combine like terms: -0.5 + 15.015625 = 14.515625
15.015625 + -7.75y + y2 = 14.515625

Factor a perfect square on the left side:
(y + -3.875)(y + -3.875) = 14.515625

Calculate the square root of the right side: 3.809937664

Break this problem into two subproblems by setting 
(y + -3.875) equal to 3.809937664 and -3.809937664.

Subproblem 1

y + -3.875 = 3.809937664 Simplifying y + -3.875 = 3.809937664 Reorder the terms: -3.875 + y = 3.809937664 Solving -3.875 + y = 3.809937664 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + y = 3.809937664 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + y = 3.809937664 + 3.875 y = 3.809937664 + 3.875 Combine like terms: 3.809937664 + 3.875 = 7.684937664 y = 7.684937664 Simplifying y = 7.684937664

Subproblem 2

y + -3.875 = -3.809937664 Simplifying y + -3.875 = -3.809937664 Reorder the terms: -3.875 + y = -3.809937664 Solving -3.875 + y = -3.809937664 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + y = -3.809937664 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + y = -3.809937664 + 3.875 y = -3.809937664 + 3.875 Combine like terms: -3.809937664 + 3.875 = 0.065062336 y = 0.065062336 Simplifying y = 0.065062336

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.684937664, 0.065062336}

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