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Simplifying (4 + -1z)(3z + -5) = 0 Reorder the terms: (4 + -1z)(-5 + 3z) = 0 Multiply (4 + -1z) * (-5 + 3z) (4(-5 + 3z) + -1z * (-5 + 3z)) = 0 ((-5 * 4 + 3z * 4) + -1z * (-5 + 3z)) = 0 ((-20 + 12z) + -1z * (-5 + 3z)) = 0 (-20 + 12z + (-5 * -1z + 3z * -1z)) = 0 (-20 + 12z + (5z + -3z2)) = 0 Combine like terms: 12z + 5z = 17z (-20 + 17z + -3z2) = 0 Solving -20 + 17z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + z)(5 + -3z) = 0Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve: Simplifying -4 + z = 0 Solving -4 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + z = 0 + 4 z = 0 + 4 Combine like terms: 0 + 4 = 4 z = 4 Simplifying z = 4Subproblem 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 = {4, 1.666666667}
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