4y^2=10-3y

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Solution for 4y^2=10-3y equation:


Simplifying
4y2 = 10 + -3y

Solving
4y2 = 10 + -3y

Solving for variable 'y'.

Reorder the terms:
-10 + 3y + 4y2 = 10 + -3y + -10 + 3y

Reorder the terms:
-10 + 3y + 4y2 = 10 + -10 + -3y + 3y

Combine like terms: 10 + -10 = 0
-10 + 3y + 4y2 = 0 + -3y + 3y
-10 + 3y + 4y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-10 + 3y + 4y2 = 0

Factor a trinomial.
(-2 + -1y)(5 + -4y) = 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 '(5 + -4y)' equal to zero and attempt to solve: Simplifying 5 + -4y = 0 Solving 5 + -4y = 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 + -4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4y = 0 + -5 -4y = 0 + -5 Combine like terms: 0 + -5 = -5 -4y = -5 Divide each side by '-4'. y = 1.25 Simplifying y = 1.25

Solution

y = {-2, 1.25}

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