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

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


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

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

Multiply (4 + 5y) * (7 + -1y)
(4(7 + -1y) + 5y * (7 + -1y)) = 0
((7 * 4 + -1y * 4) + 5y * (7 + -1y)) = 0
((28 + -4y) + 5y * (7 + -1y)) = 0
(28 + -4y + (7 * 5y + -1y * 5y)) = 0
(28 + -4y + (35y + -5y2)) = 0

Combine like terms: -4y + 35y = 31y
(28 + 31y + -5y2) = 0

Solving
28 + 31y + -5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(7 + -1y)(4 + 5y) = 0


Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

Subproblem 2
Set the factor '(4 + 5y)' equal to zero and attempt to solve:

Simplifying
4 + 5y = 0

Solving
4 + 5y = 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 + 5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5y = 0 + -4
5y = 0 + -4

Combine like terms: 0 + -4 = -4
5y = -4

Divide each side by '5'.
y = -0.8

Simplifying
y = -0.8
Solution
y = {7, -0.8}

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