4y^2-9y=-5

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Solution for 4y^2-9y=-5 equation:


Simplifying
4y2 + -9y = -5

Reorder the terms:
-9y + 4y2 = -5

Solving
-9y + 4y2 = -5

Solving for variable 'y'.

Reorder the terms:
5 + -9y + 4y2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -9y + 4y2 = 0

Factor a trinomial.
(1 + -1y)(5 + -4y) = 0

Subproblem 1

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Subproblem 2

Set the factor '(5 + -4y)' equal to zero and attempt to solve: Simplifying 5 + -4y = 0 Solving 5 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4y = 0 + -5 -4y = 0 + -5 Combine like terms: 0 + -5 = -5 -4y = -5 Divide each side by '-4'. y = 1.25 Simplifying y = 1.25

Solution

y = {1, 1.25}

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