(4y+7)(5-y)=0

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Solution for (4y+7)(5-y)=0 equation: 


Simplifying
(4y + 7)(5 + -1y) = 0

Reorder the terms:
(7 + 4y)(5 + -1y) = 0

Multiply (7 + 4y) * (5 + -1y)
(7(5 + -1y) + 4y * (5 + -1y)) = 0
((5 * 7 + -1y * 7) + 4y * (5 + -1y)) = 0
((35 + -7y) + 4y * (5 + -1y)) = 0
(35 + -7y + (5 * 4y + -1y * 4y)) = 0
(35 + -7y + (20y + -4y2)) = 0

Combine like terms: -7y + 20y = 13y
(35 + 13y + -4y2) = 0

Solving
35 + 13y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(7 + 4y) = 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 + 4y)' equal to zero and attempt to solve:

Simplifying
7 + 4y = 0

Solving
7 + 4y = 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 + 4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4y = 0 + -7
4y = 0 + -7

Combine like terms: 0 + -7 = -7
4y = -7

Divide each side by '4'.
y = -1.75

Simplifying
y = -1.75
Solution
y = {5, -1.75}

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