5y(y-2)=4-2y

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Solution for 5y(y-2)=4-2y equation:


Simplifying
5y(y + -2) = 4 + -2y

Reorder the terms:
5y(-2 + y) = 4 + -2y
(-2 * 5y + y * 5y) = 4 + -2y
(-10y + 5y2) = 4 + -2y

Solving
-10y + 5y2 = 4 + -2y

Solving for variable 'y'.

Reorder the terms:
-4 + -10y + 2y + 5y2 = 4 + -2y + -4 + 2y

Combine like terms: -10y + 2y = -8y
-4 + -8y + 5y2 = 4 + -2y + -4 + 2y

Reorder the terms:
-4 + -8y + 5y2 = 4 + -4 + -2y + 2y

Combine like terms: 4 + -4 = 0
-4 + -8y + 5y2 = 0 + -2y + 2y
-4 + -8y + 5y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-4 + -8y + 5y2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 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 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {-0.4, 2}

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