(4y+2)(7-y)=0

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Solution for (4y+2)(7-y)=0 equation: 


Simplifying
(4y + 2)(7 + -1y) = 0

Reorder the terms:
(2 + 4y)(7 + -1y) = 0

Multiply (2 + 4y) * (7 + -1y)
(2(7 + -1y) + 4y * (7 + -1y)) = 0
((7 * 2 + -1y * 2) + 4y * (7 + -1y)) = 0
((14 + -2y) + 4y * (7 + -1y)) = 0
(14 + -2y + (7 * 4y + -1y * 4y)) = 0
(14 + -2y + (28y + -4y2)) = 0

Combine like terms: -2y + 28y = 26y
(14 + 26y + -4y2) = 0

Solving
14 + 26y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 13y + -2y2) = 0

Factor a trinomial.
2((7 + -1y)(1 + 2y)) = 0

Ignore the factor 2.

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 + 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 = {7, -0.5}

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