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Simplifying (8 + -1z)(2z + -5) = 0 Reorder the terms: (8 + -1z)(-5 + 2z) = 0 Multiply (8 + -1z) * (-5 + 2z) (8(-5 + 2z) + -1z * (-5 + 2z)) = 0 ((-5 * 8 + 2z * 8) + -1z * (-5 + 2z)) = 0 ((-40 + 16z) + -1z * (-5 + 2z)) = 0 (-40 + 16z + (-5 * -1z + 2z * -1z)) = 0 (-40 + 16z + (5z + -2z2)) = 0 Combine like terms: 16z + 5z = 21z (-40 + 21z + -2z2) = 0 Solving -40 + 21z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + z)(5 + -2z) = 0Subproblem 1
Set the factor '(-8 + z)' equal to zero and attempt to solve: Simplifying -8 + z = 0 Solving -8 + z = 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 + z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z = 0 + 8 z = 0 + 8 Combine like terms: 0 + 8 = 8 z = 8 Simplifying z = 8Subproblem 2
Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 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 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {8, 2.5}
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