2y^2+5y=3

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Solution for 2y^2+5y=3 equation:


Simplifying
2y2 + 5y = 3

Reorder the terms:
5y + 2y2 = 3

Solving
5y + 2y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + 5y + 2y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 5y + 2y2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 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 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5

Solution

y = {-3, 0.5}

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