(3y-7)(8-y)=0

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Solution for (3y-7)(8-y)=0 equation: 


Simplifying
(3y + -7)(8 + -1y) = 0

Reorder the terms:
(-7 + 3y)(8 + -1y) = 0

Multiply (-7 + 3y) * (8 + -1y)
(-7(8 + -1y) + 3y * (8 + -1y)) = 0
((8 * -7 + -1y * -7) + 3y * (8 + -1y)) = 0
((-56 + 7y) + 3y * (8 + -1y)) = 0
(-56 + 7y + (8 * 3y + -1y * 3y)) = 0
(-56 + 7y + (24y + -3y2)) = 0

Combine like terms: 7y + 24y = 31y
(-56 + 31y + -3y2) = 0

Solving
-56 + 31y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-8 + y)(7 + -3y) = 0


Subproblem 1
Set the factor '(-8 + y)' equal to zero and attempt to solve:

Simplifying
-8 + y = 0

Solving
-8 + y = 0

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

Add '8' to each side of the equation.
-8 + 8 + y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + y = 0 + 8
y = 0 + 8

Combine like terms: 0 + 8 = 8
y = 8

Simplifying
y = 8

Subproblem 2
Set the factor '(7 + -3y)' equal to zero and attempt to solve:

Simplifying
7 + -3y = 0

Solving
7 + -3y = 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 + -3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3y = 0 + -7
-3y = 0 + -7

Combine like terms: 0 + -7 = -7
-3y = -7

Divide each side by '-3'.
y = 2.333333333

Simplifying
y = 2.333333333
Solution
y = {8, 2.333333333}

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