2w^2-6=-w

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Solution for 2w^2-6=-w equation:


Simplifying
2w2 + -6 = -1w

Reorder the terms:
-6 + 2w2 = -1w

Solving
-6 + 2w2 = -1w

Solving for variable 'w'.

Reorder the terms:
-6 + w + 2w2 = -1w + w

Combine like terms: -1w + w = 0
-6 + w + 2w2 = 0

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

Subproblem 1

Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2

Subproblem 2

Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5

Solution

w = {-2, 1.5}

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