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Simplifying (3z + -5)(7 + z) = 0 Reorder the terms: (-5 + 3z)(7 + z) = 0 Multiply (-5 + 3z) * (7 + z) (-5(7 + z) + 3z * (7 + z)) = 0 ((7 * -5 + z * -5) + 3z * (7 + z)) = 0 ((-35 + -5z) + 3z * (7 + z)) = 0 (-35 + -5z + (7 * 3z + z * 3z)) = 0 (-35 + -5z + (21z + 3z2)) = 0 Combine like terms: -5z + 21z = 16z (-35 + 16z + 3z2) = 0 Solving -35 + 16z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -1z)(5 + -3z) = 0Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 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 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {-7, 1.666666667}
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