20y^2=53y+450

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Solution for 20y^2=53y+450 equation:


Simplifying
20y2 = 53y + 450

Reorder the terms:
20y2 = 450 + 53y

Solving
20y2 = 450 + 53y

Solving for variable 'y'.

Reorder the terms:
-450 + -53y + 20y2 = 450 + 53y + -450 + -53y

Reorder the terms:
-450 + -53y + 20y2 = 450 + -450 + 53y + -53y

Combine like terms: 450 + -450 = 0
-450 + -53y + 20y2 = 0 + 53y + -53y
-450 + -53y + 20y2 = 53y + -53y

Combine like terms: 53y + -53y = 0
-450 + -53y + 20y2 = 0

Factor a trinomial.
(-18 + -5y)(25 + -4y) = 0

Subproblem 1

Set the factor '(-18 + -5y)' equal to zero and attempt to solve: Simplifying -18 + -5y = 0 Solving -18 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -5y = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -5y = 0 + 18 -5y = 0 + 18 Combine like terms: 0 + 18 = 18 -5y = 18 Divide each side by '-5'. y = -3.6 Simplifying y = -3.6

Subproblem 2

Set the factor '(25 + -4y)' equal to zero and attempt to solve: Simplifying 25 + -4y = 0 Solving 25 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -4y = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -4y = 0 + -25 -4y = 0 + -25 Combine like terms: 0 + -25 = -25 -4y = -25 Divide each side by '-4'. y = 6.25 Simplifying y = 6.25

Solution

y = {-3.6, 6.25}

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