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Simplifying (3z + -2)(5 + -1z) = 0 Reorder the terms: (-2 + 3z)(5 + -1z) = 0 Multiply (-2 + 3z) * (5 + -1z) (-2(5 + -1z) + 3z * (5 + -1z)) = 0 ((5 * -2 + -1z * -2) + 3z * (5 + -1z)) = 0 ((-10 + 2z) + 3z * (5 + -1z)) = 0 (-10 + 2z + (5 * 3z + -1z * 3z)) = 0 (-10 + 2z + (15z + -3z2)) = 0 Combine like terms: 2z + 15z = 17z (-10 + 17z + -3z2) = 0 Solving -10 + 17z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + z)(2 + -3z) = 0Subproblem 1
Set the factor '(-5 + z)' equal to zero and attempt to solve: Simplifying -5 + z = 0 Solving -5 + z = 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 + z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z = 0 + 5 z = 0 + 5 Combine like terms: 0 + 5 = 5 z = 5 Simplifying z = 5Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {5, 0.6666666667}
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