(4y+2)(4-y)=0

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Solution for (4y+2)(4-y)=0 equation: 


Simplifying
(4y + 2)(4 + -1y) = 0

Reorder the terms:
(2 + 4y)(4 + -1y) = 0

Multiply (2 + 4y) * (4 + -1y)
(2(4 + -1y) + 4y * (4 + -1y)) = 0
((4 * 2 + -1y * 2) + 4y * (4 + -1y)) = 0
((8 + -2y) + 4y * (4 + -1y)) = 0
(8 + -2y + (4 * 4y + -1y * 4y)) = 0
(8 + -2y + (16y + -4y2)) = 0

Combine like terms: -2y + 16y = 14y
(8 + 14y + -4y2) = 0

Solving
8 + 14y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 7y + -2y2) = 0

Factor a trinomial.
2((4 + -1y)(1 + 2y)) = 0

Ignore the factor 2.

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

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4

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

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {4, -0.5}

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