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Simplifying (8y + -1z)(7y + -1z) = 0 Multiply (8y + -1z) * (7y + -1z) (8y * (7y + -1z) + -1z * (7y + -1z)) = 0 ((7y * 8y + -1z * 8y) + -1z * (7y + -1z)) = 0 Reorder the terms: ((-8yz + 56y2) + -1z * (7y + -1z)) = 0 ((-8yz + 56y2) + -1z * (7y + -1z)) = 0 (-8yz + 56y2 + (7y * -1z + -1z * -1z)) = 0 (-8yz + 56y2 + (-7yz + 1z2)) = 0 Reorder the terms: (-8yz + -7yz + 56y2 + 1z2) = 0 Combine like terms: -8yz + -7yz = -15yz (-15yz + 56y2 + 1z2) = 0 Solving -15yz + 56y2 + 1z2 = 0 Solving for variable 'y'. Factor a trinomial. (7y + -1z)(8y + -1z) = 0Subproblem 1
Set the factor '(7y + -1z)' equal to zero and attempt to solve: Simplifying 7y + -1z = 0 Solving 7y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 7y + -1z + z = 0 + z Combine like terms: -1z + z = 0 7y + 0 = 0 + z 7y = 0 + z Remove the zero: 7y = z Divide each side by '7'. y = 0.1428571429z Simplifying y = 0.1428571429zSubproblem 2
Set the factor '(8y + -1z)' equal to zero and attempt to solve: Simplifying 8y + -1z = 0 Solving 8y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 8y + -1z + z = 0 + z Combine like terms: -1z + z = 0 8y + 0 = 0 + z 8y = 0 + z Remove the zero: 8y = z Divide each side by '8'. y = 0.125z Simplifying y = 0.125zSolution
y = {0.1428571429z, 0.125z}
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