(4y+1)(8-y)=0

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Solution for (4y+1)(8-y)=0 equation: 


Simplifying
(4y + 1)(8 + -1y) = 0

Reorder the terms:
(1 + 4y)(8 + -1y) = 0

Multiply (1 + 4y) * (8 + -1y)
(1(8 + -1y) + 4y * (8 + -1y)) = 0
((8 * 1 + -1y * 1) + 4y * (8 + -1y)) = 0
((8 + -1y) + 4y * (8 + -1y)) = 0
(8 + -1y + (8 * 4y + -1y * 4y)) = 0
(8 + -1y + (32y + -4y2)) = 0

Combine like terms: -1y + 32y = 31y
(8 + 31y + -4y2) = 0

Solving
8 + 31y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y)(1 + 4y) = 0


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

Simplifying
8 + -1y = 0

Solving
8 + -1y = 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 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y = 0 + -1
4y = 0 + -1

Combine like terms: 0 + -1 = -1
4y = -1

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {8, -0.25}

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