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Simplifying (3 + -1z)(5z + -8) = 0 Reorder the terms: (3 + -1z)(-8 + 5z) = 0 Multiply (3 + -1z) * (-8 + 5z) (3(-8 + 5z) + -1z * (-8 + 5z)) = 0 ((-8 * 3 + 5z * 3) + -1z * (-8 + 5z)) = 0 ((-24 + 15z) + -1z * (-8 + 5z)) = 0 (-24 + 15z + (-8 * -1z + 5z * -1z)) = 0 (-24 + 15z + (8z + -5z2)) = 0 Combine like terms: 15z + 8z = 23z (-24 + 23z + -5z2) = 0 Solving -24 + 23z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + z)(8 + -5z) = 0Subproblem 1
Set the factor '(-3 + z)' equal to zero and attempt to solve: Simplifying -3 + z = 0 Solving -3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0 + 3 z = 0 + 3 Combine like terms: 0 + 3 = 3 z = 3 Simplifying z = 3Subproblem 2
Set the factor '(8 + -5z)' equal to zero and attempt to solve: Simplifying 8 + -5z = 0 Solving 8 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5z = 0 + -8 -5z = 0 + -8 Combine like terms: 0 + -8 = -8 -5z = -8 Divide each side by '-5'. z = 1.6 Simplifying z = 1.6Solution
z = {3, 1.6}
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