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Simplifying (8 + z)(3z + -5) = 0 Reorder the terms: (8 + z)(-5 + 3z) = 0 Multiply (8 + z) * (-5 + 3z) (8(-5 + 3z) + z(-5 + 3z)) = 0 ((-5 * 8 + 3z * 8) + z(-5 + 3z)) = 0 ((-40 + 24z) + z(-5 + 3z)) = 0 (-40 + 24z + (-5 * z + 3z * z)) = 0 (-40 + 24z + (-5z + 3z2)) = 0 Combine like terms: 24z + -5z = 19z (-40 + 19z + 3z2) = 0 Solving -40 + 19z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -1z)(5 + -3z) = 0Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 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 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8Subproblem 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 = {-8, 1.666666667}
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