5y(y+7)=2(y+7)

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Solution for 5y(y+7)=2(y+7) equation: 


Simplifying
5y(y + 7) = 2(y + 7)

Reorder the terms:
5y(7 + y) = 2(y + 7)
(7 * 5y + y * 5y) = 2(y + 7)
(35y + 5y2) = 2(y + 7)

Reorder the terms:
35y + 5y2 = 2(7 + y)
35y + 5y2 = (7 * 2 + y * 2)
35y + 5y2 = (14 + 2y)

Solving
35y + 5y2 = 14 + 2y

Solving for variable 'y'.

Reorder the terms:
-14 + 35y + -2y + 5y2 = 14 + 2y + -14 + -2y

Combine like terms: 35y + -2y = 33y
-14 + 33y + 5y2 = 14 + 2y + -14 + -2y

Reorder the terms:
-14 + 33y + 5y2 = 14 + -14 + 2y + -2y

Combine like terms: 14 + -14 = 0
-14 + 33y + 5y2 = 0 + 2y + -2y
-14 + 33y + 5y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-14 + 33y + 5y2 = 0

Factor a trinomial.
(-7 + -1y)(2 + -5y) = 0


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 '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 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 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {-7, 0.4}

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