(3y+7)(4-y)=0

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Solution for (3y+7)(4-y)=0 equation: 


Simplifying
(3y + 7)(4 + -1y) = 0

Reorder the terms:
(7 + 3y)(4 + -1y) = 0

Multiply (7 + 3y) * (4 + -1y)
(7(4 + -1y) + 3y * (4 + -1y)) = 0
((4 * 7 + -1y * 7) + 3y * (4 + -1y)) = 0
((28 + -7y) + 3y * (4 + -1y)) = 0
(28 + -7y + (4 * 3y + -1y * 3y)) = 0
(28 + -7y + (12y + -3y2)) = 0

Combine like terms: -7y + 12y = 5y
(28 + 5y + -3y2) = 0

Solving
28 + 5y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y)(7 + 3y) = 0


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 '(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 = {4, -2.333333333}

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