-2y=5y^2-7

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


Simplifying
-2y = 5y2 + -7

Reorder the terms:
-2y = -7 + 5y2

Solving
-2y = -7 + 5y2

Solving for variable 'y'.

Reorder the terms:
7 + -2y + -5y2 = -7 + 5y2 + 7 + -5y2

Reorder the terms:
7 + -2y + -5y2 = -7 + 7 + 5y2 + -5y2

Combine like terms: -7 + 7 = 0
7 + -2y + -5y2 = 0 + 5y2 + -5y2
7 + -2y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
7 + -2y + -5y2 = 0

Factor a trinomial.
(1 + -1y)(7 + 5y) = 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 '(7 + 5y)' equal to zero and attempt to solve: Simplifying 7 + 5y = 0 Solving 7 + 5y = 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 + 5y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5y = 0 + -7 5y = 0 + -7 Combine like terms: 0 + -7 = -7 5y = -7 Divide each side by '5'. y = -1.4 Simplifying y = -1.4

Solution

y = {1, -1.4}

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