(5+y)(3y-7)=0

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Solution for (5+y)(3y-7)=0 equation: 


Simplifying
(5 + y)(3y + -7) = 0

Reorder the terms:
(5 + y)(-7 + 3y) = 0

Multiply (5 + y) * (-7 + 3y)
(5(-7 + 3y) + y(-7 + 3y)) = 0
((-7 * 5 + 3y * 5) + y(-7 + 3y)) = 0
((-35 + 15y) + y(-7 + 3y)) = 0
(-35 + 15y + (-7 * y + 3y * y)) = 0
(-35 + 15y + (-7y + 3y2)) = 0

Combine like terms: 15y + -7y = 8y
(-35 + 8y + 3y2) = 0

Solving
-35 + 8y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -1y)(7 + -3y) = 0


Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5

Subproblem 2
Set the factor '(7 + -3y)' equal to zero and attempt to solve:

Simplifying
7 + -3y = 0

Solving
7 + -3y = 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 + -3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3y = 0 + -7
-3y = 0 + -7

Combine like terms: 0 + -7 = -7
-3y = -7

Divide each side by '-3'.
y = 2.333333333

Simplifying
y = 2.333333333
Solution
y = {-5, 2.333333333}

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