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Simplifying 4z2 + 3zw + -1w2 = 0 Reorder the terms: 3wz + -1w2 + 4z2 = 0 Solving 3wz + -1w2 + 4z2 = 0 Solving for variable 'w'. Factor a trinomial. (-1w + -1z)(w + -4z) = 0Subproblem 1
Set the factor '(-1w + -1z)' equal to zero and attempt to solve: Simplifying -1w + -1z = 0 Solving -1w + -1z = 0 Move all terms containing w to the left, all other terms to the right. Add 'z' to each side of the equation. -1w + -1z + z = 0 + z Combine like terms: -1z + z = 0 -1w + 0 = 0 + z -1w = 0 + z Remove the zero: -1w = z Divide each side by '-1'. w = -1z Simplifying w = -1zSubproblem 2
Set the factor '(w + -4z)' equal to zero and attempt to solve: Simplifying w + -4z = 0 Solving w + -4z = 0 Move all terms containing w to the left, all other terms to the right. Add '4z' to each side of the equation. w + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 w + 0 = 0 + 4z w = 0 + 4z Remove the zero: w = 4z Simplifying w = 4zSolution
w = {-1z, 4z}
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