2y(3y+5)=5y^2-7y-52

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Solution for 2y(3y+5)=5y^2-7y-52 equation: 


Simplifying
2y(3y + 5) = 5y2 + -7y + -52

Reorder the terms:
2y(5 + 3y) = 5y2 + -7y + -52
(5 * 2y + 3y * 2y) = 5y2 + -7y + -52
(10y + 6y2) = 5y2 + -7y + -52

Reorder the terms:
10y + 6y2 = -52 + -7y + 5y2

Solving
10y + 6y2 = -52 + -7y + 5y2

Solving for variable 'y'.

Reorder the terms:
52 + 10y + 7y + 6y2 + -5y2 = -52 + -7y + 5y2 + 52 + 7y + -5y2

Combine like terms: 10y + 7y = 17y
52 + 17y + 6y2 + -5y2 = -52 + -7y + 5y2 + 52 + 7y + -5y2

Combine like terms: 6y2 + -5y2 = 1y2
52 + 17y + 1y2 = -52 + -7y + 5y2 + 52 + 7y + -5y2

Reorder the terms:
52 + 17y + 1y2 = -52 + 52 + -7y + 7y + 5y2 + -5y2

Combine like terms: -52 + 52 = 0
52 + 17y + 1y2 = 0 + -7y + 7y + 5y2 + -5y2
52 + 17y + 1y2 = -7y + 7y + 5y2 + -5y2

Combine like terms: -7y + 7y = 0
52 + 17y + 1y2 = 0 + 5y2 + -5y2
52 + 17y + 1y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
52 + 17y + 1y2 = 0

Factor a trinomial.
(13 + y)(4 + y) = 0


Subproblem 1
Set the factor '(13 + y)' equal to zero and attempt to solve:

Simplifying
13 + y = 0

Solving
13 + y = 0

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

Add '-13' to each side of the equation.
13 + -13 + y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + y = 0 + -13
y = 0 + -13

Combine like terms: 0 + -13 = -13
y = -13

Simplifying
y = -13

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

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

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {-13, -4}

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