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Simplifying (-2z + -7)(-8z + 5) = 0 Reorder the terms: (-7 + -2z)(-8z + 5) = 0 Reorder the terms: (-7 + -2z)(5 + -8z) = 0 Multiply (-7 + -2z) * (5 + -8z) (-7(5 + -8z) + -2z * (5 + -8z)) = 0 ((5 * -7 + -8z * -7) + -2z * (5 + -8z)) = 0 ((-35 + 56z) + -2z * (5 + -8z)) = 0 (-35 + 56z + (5 * -2z + -8z * -2z)) = 0 (-35 + 56z + (-10z + 16z2)) = 0 Combine like terms: 56z + -10z = 46z (-35 + 46z + 16z2) = 0 Solving -35 + 46z + 16z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -2z)(5 + -8z) = 0Subproblem 1
Set the factor '(-7 + -2z)' equal to zero and attempt to solve: Simplifying -7 + -2z = 0 Solving -7 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2z = 0 + 7 -2z = 0 + 7 Combine like terms: 0 + 7 = 7 -2z = 7 Divide each side by '-2'. z = -3.5 Simplifying z = -3.5Subproblem 2
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 = 0.625Solution
z = {-3.5, 0.625}
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