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

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


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

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

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

Combine like terms: -7y + 4y = -3y
(-14 + -3y + 2y2) = 0

Solving
-14 + -3y + 2y2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-2, 3.5}

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