2y-3=8y^2-6

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Solution for 2y-3=8y^2-6 equation:


Simplifying
2y + -3 = 8y2 + -6

Reorder the terms:
-3 + 2y = 8y2 + -6

Reorder the terms:
-3 + 2y = -6 + 8y2

Solving
-3 + 2y = -6 + 8y2

Solving for variable 'y'.

Reorder the terms:
-3 + 6 + 2y + -8y2 = -6 + 8y2 + 6 + -8y2

Combine like terms: -3 + 6 = 3
3 + 2y + -8y2 = -6 + 8y2 + 6 + -8y2

Reorder the terms:
3 + 2y + -8y2 = -6 + 6 + 8y2 + -8y2

Combine like terms: -6 + 6 = 0
3 + 2y + -8y2 = 0 + 8y2 + -8y2
3 + 2y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
3 + 2y + -8y2 = 0

Factor a trinomial.
(3 + -4y)(1 + 2y) = 0

Subproblem 1

Set the factor '(3 + -4y)' equal to zero and attempt to solve: Simplifying 3 + -4y = 0 Solving 3 + -4y = 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 + -4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4y = 0 + -3 -4y = 0 + -3 Combine like terms: 0 + -3 = -3 -4y = -3 Divide each side by '-4'. y = 0.75 Simplifying y = 0.75

Subproblem 2

Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5

Solution

y = {0.75, -0.5}

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