5y(y+9)=2(y+9)

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Solution for 5y(y+9)=2(y+9) equation: 


Simplifying
5y(y + 9) = 2(y + 9)

Reorder the terms:
5y(9 + y) = 2(y + 9)
(9 * 5y + y * 5y) = 2(y + 9)
(45y + 5y2) = 2(y + 9)

Reorder the terms:
45y + 5y2 = 2(9 + y)
45y + 5y2 = (9 * 2 + y * 2)
45y + 5y2 = (18 + 2y)

Solving
45y + 5y2 = 18 + 2y

Solving for variable 'y'.

Reorder the terms:
-18 + 45y + -2y + 5y2 = 18 + 2y + -18 + -2y

Combine like terms: 45y + -2y = 43y
-18 + 43y + 5y2 = 18 + 2y + -18 + -2y

Reorder the terms:
-18 + 43y + 5y2 = 18 + -18 + 2y + -2y

Combine like terms: 18 + -18 = 0
-18 + 43y + 5y2 = 0 + 2y + -2y
-18 + 43y + 5y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-18 + 43y + 5y2 = 0

Factor a trinomial.
(-9 + -1y)(2 + -5y) = 0


Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9

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 = {-9, 0.4}

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