-5y(3y-5)+4(2y+10)=

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Solution for -5y(3y-5)+4(2y+10)= equation:


Simplifying
-5y(3y + -5) + 4(2y + 10) = 0

Reorder the terms:
-5y(-5 + 3y) + 4(2y + 10) = 0
(-5 * -5y + 3y * -5y) + 4(2y + 10) = 0
(25y + -15y2) + 4(2y + 10) = 0

Reorder the terms:
25y + -15y2 + 4(10 + 2y) = 0
25y + -15y2 + (10 * 4 + 2y * 4) = 0
25y + -15y2 + (40 + 8y) = 0

Reorder the terms:
40 + 25y + 8y + -15y2 = 0

Combine like terms: 25y + 8y = 33y
40 + 33y + -15y2 = 0

Solving
40 + 33y + -15y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-2.666666667 + -2.2y + y2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -2.2y + 2.666666667 + y2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -2.2y + y2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -2.2y + y2 = 0 + 2.666666667
-2.2y + y2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-2.2y + y2 = 2.666666667

The y term is -2.2y.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2y + 1.21 + y2 = 2.666666667 + 1.21

Reorder the terms:
1.21 + -2.2y + y2 = 2.666666667 + 1.21

Combine like terms: 2.666666667 + 1.21 = 3.876666667
1.21 + -2.2y + y2 = 3.876666667

Factor a perfect square on the left side:
(y + -1.1)(y + -1.1) = 3.876666667

Calculate the square root of the right side: 1.968925257

Break this problem into two subproblems by setting 
(y + -1.1) equal to 1.968925257 and -1.968925257.

Subproblem 1

y + -1.1 = 1.968925257 Simplifying y + -1.1 = 1.968925257 Reorder the terms: -1.1 + y = 1.968925257 Solving -1.1 + y = 1.968925257 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = 1.968925257 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = 1.968925257 + 1.1 y = 1.968925257 + 1.1 Combine like terms: 1.968925257 + 1.1 = 3.068925257 y = 3.068925257 Simplifying y = 3.068925257

Subproblem 2

y + -1.1 = -1.968925257 Simplifying y + -1.1 = -1.968925257 Reorder the terms: -1.1 + y = -1.968925257 Solving -1.1 + y = -1.968925257 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = -1.968925257 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = -1.968925257 + 1.1 y = -1.968925257 + 1.1 Combine like terms: -1.968925257 + 1.1 = -0.868925257 y = -0.868925257 Simplifying y = -0.868925257

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.068925257, -0.868925257}

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