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

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


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

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

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