2y(y+4)+3(y-4)=

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Solution for 2y(y+4)+3(y-4)= equation:


Simplifying
2y(y + 4) + 3(y + -4) = 0

Reorder the terms:
2y(4 + y) + 3(y + -4) = 0
(4 * 2y + y * 2y) + 3(y + -4) = 0
(8y + 2y2) + 3(y + -4) = 0

Reorder the terms:
8y + 2y2 + 3(-4 + y) = 0
8y + 2y2 + (-4 * 3 + y * 3) = 0
8y + 2y2 + (-12 + 3y) = 0

Reorder the terms:
-12 + 8y + 3y + 2y2 = 0

Combine like terms: 8y + 3y = 11y
-12 + 11y + 2y2 = 0

Solving
-12 + 11y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-6 + 5.5y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 5.5y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 5.5y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 5.5y + y2 = 0 + 6
5.5y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
5.5y + y2 = 6

The y term is 5.5y.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5y + 7.5625 + y2 = 6 + 7.5625

Reorder the terms:
7.5625 + 5.5y + y2 = 6 + 7.5625

Combine like terms: 6 + 7.5625 = 13.5625
7.5625 + 5.5y + y2 = 13.5625

Factor a perfect square on the left side:
(y + 2.75)(y + 2.75) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(y + 2.75) equal to 3.682729966 and -3.682729966.

Subproblem 1

y + 2.75 = 3.682729966 Simplifying y + 2.75 = 3.682729966 Reorder the terms: 2.75 + y = 3.682729966 Solving 2.75 + y = 3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 3.682729966 + -2.75 y = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 y = 0.932729966 Simplifying y = 0.932729966

Subproblem 2

y + 2.75 = -3.682729966 Simplifying y + 2.75 = -3.682729966 Reorder the terms: 2.75 + y = -3.682729966 Solving 2.75 + y = -3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -3.682729966 + -2.75 y = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 y = -6.432729966 Simplifying y = -6.432729966

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.932729966, -6.432729966}

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