2y^2=-3y+35

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Solution for 2y^2=-3y+35 equation:


Simplifying
2y2 = -3y + 35

Reorder the terms:
2y2 = 35 + -3y

Solving
2y2 = 35 + -3y

Solving for variable 'y'.

Reorder the terms:
-35 + 3y + 2y2 = 35 + -3y + -35 + 3y

Reorder the terms:
-35 + 3y + 2y2 = 35 + -35 + -3y + 3y

Combine like terms: 35 + -35 = 0
-35 + 3y + 2y2 = 0 + -3y + 3y
-35 + 3y + 2y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-35 + 3y + 2y2 = 0

Factor a trinomial.
(-5 + -1y)(7 + -2y) = 0

Subproblem 1

Set the factor '(-5 + -1y)' equal to zero and attempt to solve: Simplifying -5 + -1y = 0 Solving -5 + -1y = 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 + -1y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y = 0 + 5 -1y = 0 + 5 Combine like terms: 0 + 5 = 5 -1y = 5 Divide each side by '-1'. y = -5 Simplifying y = -5

Subproblem 2

Set the factor '(7 + -2y)' equal to zero and attempt to solve: Simplifying 7 + -2y = 0 Solving 7 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2y = 0 + -7 -2y = 0 + -7 Combine like terms: 0 + -7 = -7 -2y = -7 Divide each side by '-2'. y = 3.5 Simplifying y = 3.5

Solution

y = {-5, 3.5}

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