(2y+7)(5-y)=0

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Solution for (2y+7)(5-y)=0 equation: 


Simplifying
(2y + 7)(5 + -1y) = 0

Reorder the terms:
(7 + 2y)(5 + -1y) = 0

Multiply (7 + 2y) * (5 + -1y)
(7(5 + -1y) + 2y * (5 + -1y)) = 0
((5 * 7 + -1y * 7) + 2y * (5 + -1y)) = 0
((35 + -7y) + 2y * (5 + -1y)) = 0
(35 + -7y + (5 * 2y + -1y * 2y)) = 0
(35 + -7y + (10y + -2y2)) = 0

Combine like terms: -7y + 10y = 3y
(35 + 3y + -2y2) = 0

Solving
35 + 3y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(7 + 2y) = 0


Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(7 + 2y)' equal to zero and attempt to solve:

Simplifying
7 + 2y = 0

Solving
7 + 2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2y = 0 + -7
2y = 0 + -7

Combine like terms: 0 + -7 = -7
2y = -7

Divide each side by '2'.
y = -3.5

Simplifying
y = -3.5
Solution
y = {5, -3.5}

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