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Simplifying (8z + 5)(9z + -5) = 0 Reorder the terms: (5 + 8z)(9z + -5) = 0 Reorder the terms: (5 + 8z)(-5 + 9z) = 0 Multiply (5 + 8z) * (-5 + 9z) (5(-5 + 9z) + 8z * (-5 + 9z)) = 0 ((-5 * 5 + 9z * 5) + 8z * (-5 + 9z)) = 0 ((-25 + 45z) + 8z * (-5 + 9z)) = 0 (-25 + 45z + (-5 * 8z + 9z * 8z)) = 0 (-25 + 45z + (-40z + 72z2)) = 0 Combine like terms: 45z + -40z = 5z (-25 + 5z + 72z2) = 0 Solving -25 + 5z + 72z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -8z)(5 + -9z) = 0Subproblem 1
Set the factor '(-5 + -8z)' equal to zero and attempt to solve: Simplifying -5 + -8z = 0 Solving -5 + -8z = 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 + -8z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8z = 0 + 5 -8z = 0 + 5 Combine like terms: 0 + 5 = 5 -8z = 5 Divide each side by '-8'. z = -0.625 Simplifying z = -0.625Subproblem 2
Set the factor '(5 + -9z)' equal to zero and attempt to solve: Simplifying 5 + -9z = 0 Solving 5 + -9z = 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 + -9z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9z = 0 + -5 -9z = 0 + -5 Combine like terms: 0 + -5 = -5 -9z = -5 Divide each side by '-9'. z = 0.5555555556 Simplifying z = 0.5555555556Solution
z = {-0.625, 0.5555555556}
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