10w^2-15w-10=0

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Solution for 10w^2-15w-10=0 equation:


Simplifying
10w2 + -15w + -10 = 0

Reorder the terms:
-10 + -15w + 10w2 = 0

Solving
-10 + -15w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -3w + 2w2) = 0

Factor a trinomial.
5((-1 + -2w)(2 + -1w)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5

Subproblem 2

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

Solution

w = {-0.5, 2}

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