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Simplifying (5 + -1z)(3z + -4) = 0 Reorder the terms: (5 + -1z)(-4 + 3z) = 0 Multiply (5 + -1z) * (-4 + 3z) (5(-4 + 3z) + -1z * (-4 + 3z)) = 0 ((-4 * 5 + 3z * 5) + -1z * (-4 + 3z)) = 0 ((-20 + 15z) + -1z * (-4 + 3z)) = 0 (-20 + 15z + (-4 * -1z + 3z * -1z)) = 0 (-20 + 15z + (4z + -3z2)) = 0 Combine like terms: 15z + 4z = 19z (-20 + 19z + -3z2) = 0 Solving -20 + 19z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + z)(4 + -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 '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 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 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {5, 1.333333333}
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