(2y-1)(y+9)=20y

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Solution for (2y-1)(y+9)=20y equation:


Simplifying
(2y + -1)(y + 9) = 20y

Reorder the terms:
(-1 + 2y)(y + 9) = 20y

Reorder the terms:
(-1 + 2y)(9 + y) = 20y

Multiply (-1 + 2y) * (9 + y)
(-1(9 + y) + 2y * (9 + y)) = 20y
((9 * -1 + y * -1) + 2y * (9 + y)) = 20y
((-9 + -1y) + 2y * (9 + y)) = 20y
(-9 + -1y + (9 * 2y + y * 2y)) = 20y
(-9 + -1y + (18y + 2y2)) = 20y

Combine like terms: -1y + 18y = 17y
(-9 + 17y + 2y2) = 20y

Solving
-9 + 17y + 2y2 = 20y

Solving for variable 'y'.

Reorder the terms:
-9 + 17y + -20y + 2y2 = 20y + -20y

Combine like terms: 17y + -20y = -3y
-9 + -3y + 2y2 = 20y + -20y

Combine like terms: 20y + -20y = 0
-9 + -3y + 2y2 = 0

Factor a trinomial.
(-3 + -2y)(3 + -1y) = 0

Subproblem 1

Set the factor '(-3 + -2y)' equal to zero and attempt to solve: Simplifying -3 + -2y = 0 Solving -3 + -2y = 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 + -2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2y = 0 + 3 -2y = 0 + 3 Combine like terms: 0 + 3 = 3 -2y = 3 Divide each side by '-2'. y = -1.5 Simplifying y = -1.5

Subproblem 2

Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 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 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3

Solution

y = {-1.5, 3}

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