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Simplifying (3z + -8)(z + 5) = 0 Reorder the terms: (-8 + 3z)(z + 5) = 0 Reorder the terms: (-8 + 3z)(5 + z) = 0 Multiply (-8 + 3z) * (5 + z) (-8(5 + z) + 3z * (5 + z)) = 0 ((5 * -8 + z * -8) + 3z * (5 + z)) = 0 ((-40 + -8z) + 3z * (5 + z)) = 0 (-40 + -8z + (5 * 3z + z * 3z)) = 0 (-40 + -8z + (15z + 3z2)) = 0 Combine like terms: -8z + 15z = 7z (-40 + 7z + 3z2) = 0 Solving -40 + 7z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(8 + -3z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(8 + -3z)' equal to zero and attempt to solve: Simplifying 8 + -3z = 0 Solving 8 + -3z = 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 + -3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3z = 0 + -8 -3z = 0 + -8 Combine like terms: 0 + -8 = -8 -3z = -8 Divide each side by '-3'. z = 2.666666667 Simplifying z = 2.666666667Solution
z = {-5, 2.666666667}
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