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Simplifying (10w + 3z)(w + -6z) = 0 Multiply (10w + 3z) * (w + -6z) (10w * (w + -6z) + 3z * (w + -6z)) = 0 ((w * 10w + -6z * 10w) + 3z * (w + -6z)) = 0 Reorder the terms: ((-60wz + 10w2) + 3z * (w + -6z)) = 0 ((-60wz + 10w2) + 3z * (w + -6z)) = 0 (-60wz + 10w2 + (w * 3z + -6z * 3z)) = 0 (-60wz + 10w2 + (3wz + -18z2)) = 0 Reorder the terms: (-60wz + 3wz + 10w2 + -18z2) = 0 Combine like terms: -60wz + 3wz = -57wz (-57wz + 10w2 + -18z2) = 0 Solving -57wz + 10w2 + -18z2 = 0 Solving for variable 'w'. Factor a trinomial. (w + -6z)(10w + 3z) = 0Subproblem 1
Set the factor '(w + -6z)' equal to zero and attempt to solve: Simplifying w + -6z = 0 Solving w + -6z = 0 Move all terms containing w to the left, all other terms to the right. Add '6z' to each side of the equation. w + -6z + 6z = 0 + 6z Combine like terms: -6z + 6z = 0 w + 0 = 0 + 6z w = 0 + 6z Remove the zero: w = 6z Simplifying w = 6zSubproblem 2
Set the factor '(10w + 3z)' equal to zero and attempt to solve: Simplifying 10w + 3z = 0 Solving 10w + 3z = 0 Move all terms containing w to the left, all other terms to the right. Add '-3z' to each side of the equation. 10w + 3z + -3z = 0 + -3z Combine like terms: 3z + -3z = 0 10w + 0 = 0 + -3z 10w = 0 + -3z Remove the zero: 10w = -3z Divide each side by '10'. w = -0.3z Simplifying w = -0.3zSolution
w = {6z, -0.3z}
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