2q^2+7qw-15w^2=0

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Solution for 2q^2+7qw-15w^2=0 equation:


Simplifying
2q2 + 7qw + -15w2 = 0

Reorder the terms:
7qw + 2q2 + -15w2 = 0

Solving
7qw + 2q2 + -15w2 = 0

Solving for variable 'q'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(q + 5w)' equal to zero and attempt to solve: Simplifying q + 5w = 0 Solving q + 5w = 0 Move all terms containing q to the left, all other terms to the right. Add '-5w' to each side of the equation. q + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 q + 0 = 0 + -5w q = 0 + -5w Remove the zero: q = -5w Simplifying q = -5w

Solution

q = {1.5w, -5w}

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