2y^2+10y-15=-2y^2+6y

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Solution for 2y^2+10y-15=-2y^2+6y equation:


Simplifying
2y2 + 10y + -15 = -2y2 + 6y

Reorder the terms:
-15 + 10y + 2y2 = -2y2 + 6y

Reorder the terms:
-15 + 10y + 2y2 = 6y + -2y2

Solving
-15 + 10y + 2y2 = 6y + -2y2

Solving for variable 'y'.

Reorder the terms:
-15 + 10y + -6y + 2y2 + 2y2 = 6y + -2y2 + -6y + 2y2

Combine like terms: 10y + -6y = 4y
-15 + 4y + 2y2 + 2y2 = 6y + -2y2 + -6y + 2y2

Combine like terms: 2y2 + 2y2 = 4y2
-15 + 4y + 4y2 = 6y + -2y2 + -6y + 2y2

Reorder the terms:
-15 + 4y + 4y2 = 6y + -6y + -2y2 + 2y2

Combine like terms: 6y + -6y = 0
-15 + 4y + 4y2 = 0 + -2y2 + 2y2
-15 + 4y + 4y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
-15 + 4y + 4y2 = 0

Factor a trinomial.
(-5 + -2y)(3 + -2y) = 0

Subproblem 1

Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5

Subproblem 2

Set the factor '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 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 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5

Solution

y = {-2.5, 1.5}

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