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Simplifying 90z2 + 129wz + 28w2 = 0 Reorder the terms: 129wz + 28w2 + 90z2 = 0 Solving 129wz + 28w2 + 90z2 = 0 Solving for variable 'w'. Factor a trinomial. (7w + 6z)(4w + 15z) = 0Subproblem 1
Set the factor '(7w + 6z)' equal to zero and attempt to solve: Simplifying 7w + 6z = 0 Solving 7w + 6z = 0 Move all terms containing w to the left, all other terms to the right. Add '-6z' to each side of the equation. 7w + 6z + -6z = 0 + -6z Combine like terms: 6z + -6z = 0 7w + 0 = 0 + -6z 7w = 0 + -6z Remove the zero: 7w = -6z Divide each side by '7'. w = -0.8571428571z Simplifying w = -0.8571428571zSubproblem 2
Set the factor '(4w + 15z)' equal to zero and attempt to solve: Simplifying 4w + 15z = 0 Solving 4w + 15z = 0 Move all terms containing w to the left, all other terms to the right. Add '-15z' to each side of the equation. 4w + 15z + -15z = 0 + -15z Combine like terms: 15z + -15z = 0 4w + 0 = 0 + -15z 4w = 0 + -15z Remove the zero: 4w = -15z Divide each side by '4'. w = -3.75z Simplifying w = -3.75zSolution
w = {-0.8571428571z, -3.75z}
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