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Simplifying (4y + -1z)(2y + 7z) = 0 Multiply (4y + -1z) * (2y + 7z) (4y * (2y + 7z) + -1z * (2y + 7z)) = 0 ((2y * 4y + 7z * 4y) + -1z * (2y + 7z)) = 0 Reorder the terms: ((28yz + 8y2) + -1z * (2y + 7z)) = 0 ((28yz + 8y2) + -1z * (2y + 7z)) = 0 (28yz + 8y2 + (2y * -1z + 7z * -1z)) = 0 (28yz + 8y2 + (-2yz + -7z2)) = 0 Reorder the terms: (28yz + -2yz + 8y2 + -7z2) = 0 Combine like terms: 28yz + -2yz = 26yz (26yz + 8y2 + -7z2) = 0 Solving 26yz + 8y2 + -7z2 = 0 Solving for variable 'y'. Factor a trinomial. (4y + -1z)(2y + 7z) = 0Subproblem 1
Set the factor '(4y + -1z)' equal to zero and attempt to solve: Simplifying 4y + -1z = 0 Solving 4y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 4y + -1z + z = 0 + z Combine like terms: -1z + z = 0 4y + 0 = 0 + z 4y = 0 + z Remove the zero: 4y = z Divide each side by '4'. y = 0.25z Simplifying y = 0.25zSubproblem 2
Set the factor '(2y + 7z)' equal to zero and attempt to solve: Simplifying 2y + 7z = 0 Solving 2y + 7z = 0 Move all terms containing y to the left, all other terms to the right. Add '-7z' to each side of the equation. 2y + 7z + -7z = 0 + -7z Combine like terms: 7z + -7z = 0 2y + 0 = 0 + -7z 2y = 0 + -7z Remove the zero: 2y = -7z Divide each side by '2'. y = -3.5z Simplifying y = -3.5zSolution
y = {0.25z, -3.5z}
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