(4y+6)(8-y)=0

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Solution for (4y+6)(8-y)=0 equation: 


Simplifying
(4y + 6)(8 + -1y) = 0

Reorder the terms:
(6 + 4y)(8 + -1y) = 0

Multiply (6 + 4y) * (8 + -1y)
(6(8 + -1y) + 4y * (8 + -1y)) = 0
((8 * 6 + -1y * 6) + 4y * (8 + -1y)) = 0
((48 + -6y) + 4y * (8 + -1y)) = 0
(48 + -6y + (8 * 4y + -1y * 4y)) = 0
(48 + -6y + (32y + -4y2)) = 0

Combine like terms: -6y + 32y = 26y
(48 + 26y + -4y2) = 0

Solving
48 + 26y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 13y + -2y2) = 0

Factor a trinomial.
2((8 + -1y)(3 + 2y)) = 0

Ignore the factor 2.

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 '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {8, -1.5}

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