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

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Solution for (4y+1)(7-y)=0 equation: 


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

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

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

Combine like terms: -1y + 28y = 27y
(7 + 27y + -4y2) = 0

Solving
7 + 27y + -4y2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

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 = {7, -0.25}

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