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Simplifying 4z2 + -12zw + 9w2 = 0 Reorder the terms: -12wz + 9w2 + 4z2 = 0 Solving -12wz + 9w2 + 4z2 = 0 Solving for variable 'w'. Factor a trinomial. (3w + -2z)(3w + -2z) = 0Subproblem 1
Set the factor '(3w + -2z)' equal to zero and attempt to solve: Simplifying 3w + -2z = 0 Solving 3w + -2z = 0 Move all terms containing w to the left, all other terms to the right. Add '2z' to each side of the equation. 3w + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 3w + 0 = 0 + 2z 3w = 0 + 2z Remove the zero: 3w = 2z Divide each side by '3'. w = 0.6666666667z Simplifying w = 0.6666666667zSubproblem 2
Set the factor '(3w + -2z)' equal to zero and attempt to solve: Simplifying 3w + -2z = 0 Solving 3w + -2z = 0 Move all terms containing w to the left, all other terms to the right. Add '2z' to each side of the equation. 3w + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 3w + 0 = 0 + 2z 3w = 0 + 2z Remove the zero: 3w = 2z Divide each side by '3'. w = 0.6666666667z Simplifying w = 0.6666666667zSolution
w = {0.6666666667z, 0.6666666667z}
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