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

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


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

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

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

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

Combine like terms: 4y + 14y = 18y
(28 + 18y + 2y2) = 0

Solving
28 + 18y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 9y + y2) = 0

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

Ignore the factor 2.

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

Simplifying
7 + y = 0

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

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

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

Simplifying
y = -7

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

Simplifying
2 + y = 0

Solving
2 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

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

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

Simplifying
y = -2
Solution
y = {-7, -2}

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