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

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


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

Reorder the terms:
5y(2 + y) = (y + -9)(y + -2)
(2 * 5y + y * 5y) = (y + -9)(y + -2)
(10y + 5y2) = (y + -9)(y + -2)

Reorder the terms:
10y + 5y2 = (-9 + y)(y + -2)

Reorder the terms:
10y + 5y2 = (-9 + y)(-2 + y)

Multiply (-9 + y) * (-2 + y)
10y + 5y2 = (-9(-2 + y) + y(-2 + y))
10y + 5y2 = ((-2 * -9 + y * -9) + y(-2 + y))
10y + 5y2 = ((18 + -9y) + y(-2 + y))
10y + 5y2 = (18 + -9y + (-2 * y + y * y))
10y + 5y2 = (18 + -9y + (-2y + y2))

Combine like terms: -9y + -2y = -11y
10y + 5y2 = (18 + -11y + y2)

Solving
10y + 5y2 = 18 + -11y + y2

Solving for variable 'y'.

Reorder the terms:
-18 + 10y + 11y + 5y2 + -1y2 = 18 + -11y + y2 + -18 + 11y + -1y2

Combine like terms: 10y + 11y = 21y
-18 + 21y + 5y2 + -1y2 = 18 + -11y + y2 + -18 + 11y + -1y2

Combine like terms: 5y2 + -1y2 = 4y2
-18 + 21y + 4y2 = 18 + -11y + y2 + -18 + 11y + -1y2

Reorder the terms:
-18 + 21y + 4y2 = 18 + -18 + -11y + 11y + y2 + -1y2

Combine like terms: 18 + -18 = 0
-18 + 21y + 4y2 = 0 + -11y + 11y + y2 + -1y2
-18 + 21y + 4y2 = -11y + 11y + y2 + -1y2

Combine like terms: -11y + 11y = 0
-18 + 21y + 4y2 = 0 + y2 + -1y2
-18 + 21y + 4y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-18 + 21y + 4y2 = 0

Factor a trinomial.
(-6 + -1y)(3 + -4y) = 0


Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6

Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-6, 0.75}

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