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Simplifying (4w + 5z)(4w + 5z) = 0 Multiply (4w + 5z) * (4w + 5z) (4w * (4w + 5z) + 5z * (4w + 5z)) = 0 ((4w * 4w + 5z * 4w) + 5z * (4w + 5z)) = 0 Reorder the terms: ((20wz + 16w2) + 5z * (4w + 5z)) = 0 ((20wz + 16w2) + 5z * (4w + 5z)) = 0 (20wz + 16w2 + (4w * 5z + 5z * 5z)) = 0 (20wz + 16w2 + (20wz + 25z2)) = 0 Reorder the terms: (20wz + 20wz + 16w2 + 25z2) = 0 Combine like terms: 20wz + 20wz = 40wz (40wz + 16w2 + 25z2) = 0 Solving 40wz + 16w2 + 25z2 = 0 Solving for variable 'w'. Factor a trinomial. (4w + 5z)(4w + 5z) = 0Subproblem 1
Set the factor '(4w + 5z)' equal to zero and attempt to solve: Simplifying 4w + 5z = 0 Solving 4w + 5z = 0 Move all terms containing w to the left, all other terms to the right. Add '-5z' to each side of the equation. 4w + 5z + -5z = 0 + -5z Combine like terms: 5z + -5z = 0 4w + 0 = 0 + -5z 4w = 0 + -5z Remove the zero: 4w = -5z Divide each side by '4'. w = -1.25z Simplifying w = -1.25zSubproblem 2
Set the factor '(4w + 5z)' equal to zero and attempt to solve: Simplifying 4w + 5z = 0 Solving 4w + 5z = 0 Move all terms containing w to the left, all other terms to the right. Add '-5z' to each side of the equation. 4w + 5z + -5z = 0 + -5z Combine like terms: 5z + -5z = 0 4w + 0 = 0 + -5z 4w = 0 + -5z Remove the zero: 4w = -5z Divide each side by '4'. w = -1.25z Simplifying w = -1.25zSolution
w = {-1.25z, -1.25z}
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