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

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


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

Multiply (7 + -2y) * (5 + y)
(7(5 + y) + -2y * (5 + y)) = 0
((5 * 7 + y * 7) + -2y * (5 + y)) = 0
((35 + 7y) + -2y * (5 + y)) = 0
(35 + 7y + (5 * -2y + y * -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.
(7 + -2y)(5 + y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 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 + y = 0 + -5

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

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

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

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