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Simplifying (5z + 7y)(5z + 7y) = 0 Reorder the terms: (7y + 5z)(5z + 7y) = 0 Reorder the terms: (7y + 5z)(7y + 5z) = 0 Multiply (7y + 5z) * (7y + 5z) (7y * (7y + 5z) + 5z * (7y + 5z)) = 0 ((7y * 7y + 5z * 7y) + 5z * (7y + 5z)) = 0 Reorder the terms: ((35yz + 49y2) + 5z * (7y + 5z)) = 0 ((35yz + 49y2) + 5z * (7y + 5z)) = 0 (35yz + 49y2 + (7y * 5z + 5z * 5z)) = 0 (35yz + 49y2 + (35yz + 25z2)) = 0 Reorder the terms: (35yz + 35yz + 49y2 + 25z2) = 0 Combine like terms: 35yz + 35yz = 70yz (70yz + 49y2 + 25z2) = 0 Solving 70yz + 49y2 + 25z2 = 0 Solving for variable 'y'. Factor a trinomial. (7y + 5z)(7y + 5z) = 0Subproblem 1
Set the factor '(7y + 5z)' equal to zero and attempt to solve: Simplifying 7y + 5z = 0 Solving 7y + 5z = 0 Move all terms containing y to the left, all other terms to the right. Add '-5z' to each side of the equation. 7y + 5z + -5z = 0 + -5z Combine like terms: 5z + -5z = 0 7y + 0 = 0 + -5z 7y = 0 + -5z Remove the zero: 7y = -5z Divide each side by '7'. y = -0.7142857143z Simplifying y = -0.7142857143zSubproblem 2
Set the factor '(7y + 5z)' equal to zero and attempt to solve: Simplifying 7y + 5z = 0 Solving 7y + 5z = 0 Move all terms containing y to the left, all other terms to the right. Add '-5z' to each side of the equation. 7y + 5z + -5z = 0 + -5z Combine like terms: 5z + -5z = 0 7y + 0 = 0 + -5z 7y = 0 + -5z Remove the zero: 7y = -5z Divide each side by '7'. y = -0.7142857143z Simplifying y = -0.7142857143zSolution
y = {-0.7142857143z, -0.7142857143z}
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