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Simplifying (1 + -1z)(5z + -7) = 0 Reorder the terms: (1 + -1z)(-7 + 5z) = 0 Multiply (1 + -1z) * (-7 + 5z) (1(-7 + 5z) + -1z * (-7 + 5z)) = 0 ((-7 * 1 + 5z * 1) + -1z * (-7 + 5z)) = 0 ((-7 + 5z) + -1z * (-7 + 5z)) = 0 (-7 + 5z + (-7 * -1z + 5z * -1z)) = 0 (-7 + 5z + (7z + -5z2)) = 0 Combine like terms: 5z + 7z = 12z (-7 + 12z + -5z2) = 0 Solving -7 + 12z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + 5z)(1 + -1z) = 0Subproblem 1
Set the factor '(-7 + 5z)' equal to zero and attempt to solve: Simplifying -7 + 5z = 0 Solving -7 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 5z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5z = 0 + 7 5z = 0 + 7 Combine like terms: 0 + 7 = 7 5z = 7 Divide each side by '5'. z = 1.4 Simplifying z = 1.4Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {1.4, 1}
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