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Simplifying 3(3z + -5)(1z + 1) = 0 Reorder the terms: 3(-5 + 3z)(1z + 1) = 0 Reorder the terms: 3(-5 + 3z)(1 + 1z) = 0 Multiply (-5 + 3z) * (1 + 1z) 3(-5(1 + 1z) + 3z * (1 + 1z)) = 0 3((1 * -5 + 1z * -5) + 3z * (1 + 1z)) = 0 3((-5 + -5z) + 3z * (1 + 1z)) = 0 3(-5 + -5z + (1 * 3z + 1z * 3z)) = 0 3(-5 + -5z + (3z + 3z2)) = 0 Combine like terms: -5z + 3z = -2z 3(-5 + -2z + 3z2) = 0 (-5 * 3 + -2z * 3 + 3z2 * 3) = 0 (-15 + -6z + 9z2) = 0 Solving -15 + -6z + 9z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -2z + 3z2) = 0 Factor a trinomial. 3((-1 + -1z)(5 + -3z)) = 0 Ignore the factor 3.Subproblem 1
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 = -1Subproblem 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 = {-1, 1.666666667}
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