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Simplifying (3 + -1z)(3z + -7) = 0 Reorder the terms: (3 + -1z)(-7 + 3z) = 0 Multiply (3 + -1z) * (-7 + 3z) (3(-7 + 3z) + -1z * (-7 + 3z)) = 0 ((-7 * 3 + 3z * 3) + -1z * (-7 + 3z)) = 0 ((-21 + 9z) + -1z * (-7 + 3z)) = 0 (-21 + 9z + (-7 * -1z + 3z * -1z)) = 0 (-21 + 9z + (7z + -3z2)) = 0 Combine like terms: 9z + 7z = 16z (-21 + 16z + -3z2) = 0 Solving -21 + 16z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + z)(7 + -3z) = 0Subproblem 1
Set the factor '(-3 + z)' equal to zero and attempt to solve: Simplifying -3 + z = 0 Solving -3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0 + 3 z = 0 + 3 Combine like terms: 0 + 3 = 3 z = 3 Simplifying z = 3Subproblem 2
Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 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 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {3, 2.333333333}
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