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Simplifying (3y + -1z)(y + -7z) = 0 Multiply (3y + -1z) * (y + -7z) (3y * (y + -7z) + -1z * (y + -7z)) = 0 ((y * 3y + -7z * 3y) + -1z * (y + -7z)) = 0 Reorder the terms: ((-21yz + 3y2) + -1z * (y + -7z)) = 0 ((-21yz + 3y2) + -1z * (y + -7z)) = 0 (-21yz + 3y2 + (y * -1z + -7z * -1z)) = 0 (-21yz + 3y2 + (-1yz + 7z2)) = 0 Reorder the terms: (-21yz + -1yz + 3y2 + 7z2) = 0 Combine like terms: -21yz + -1yz = -22yz (-22yz + 3y2 + 7z2) = 0 Solving -22yz + 3y2 + 7z2 = 0 Solving for variable 'y'. Factor a trinomial. (y + -7z)(3y + -1z) = 0Subproblem 1
Set the factor '(y + -7z)' equal to zero and attempt to solve: Simplifying y + -7z = 0 Solving y + -7z = 0 Move all terms containing y to the left, all other terms to the right. Add '7z' to each side of the equation. y + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 y + 0 = 0 + 7z y = 0 + 7z Remove the zero: y = 7z Simplifying y = 7zSubproblem 2
Set the factor '(3y + -1z)' equal to zero and attempt to solve: Simplifying 3y + -1z = 0 Solving 3y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 3y + -1z + z = 0 + z Combine like terms: -1z + z = 0 3y + 0 = 0 + z 3y = 0 + z Remove the zero: 3y = z Divide each side by '3'. y = 0.3333333333z Simplifying y = 0.3333333333zSolution
y = {7z, 0.3333333333z}
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