7y^2=-5y+18

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Solution for 7y^2=-5y+18 equation:


Simplifying
7y2 = -5y + 18

Reorder the terms:
7y2 = 18 + -5y

Solving
7y2 = 18 + -5y

Solving for variable 'y'.

Reorder the terms:
-18 + 5y + 7y2 = 18 + -5y + -18 + 5y

Reorder the terms:
-18 + 5y + 7y2 = 18 + -18 + -5y + 5y

Combine like terms: 18 + -18 = 0
-18 + 5y + 7y2 = 0 + -5y + 5y
-18 + 5y + 7y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
-18 + 5y + 7y2 = 0

Factor a trinomial.
(-2 + -1y)(9 + -7y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(9 + -7y)' equal to zero and attempt to solve: Simplifying 9 + -7y = 0 Solving 9 + -7y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7y = 0 + -9 -7y = 0 + -9 Combine like terms: 0 + -9 = -9 -7y = -9 Divide each side by '-7'. y = 1.285714286 Simplifying y = 1.285714286

Solution

y = {-2, 1.285714286}

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