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Simplifying 10z2 + 9z + -16 = 20 Reorder the terms: -16 + 9z + 10z2 = 20 Solving -16 + 9z + 10z2 = 20 Solving for variable 'z'. Reorder the terms: -16 + -20 + 9z + 10z2 = 20 + -20 Combine like terms: -16 + -20 = -36 -36 + 9z + 10z2 = 20 + -20 Combine like terms: 20 + -20 = 0 -36 + 9z + 10z2 = 0 Factor a trinomial. (-12 + -5z)(3 + -2z) = 0Subproblem 1
Set the factor '(-12 + -5z)' equal to zero and attempt to solve: Simplifying -12 + -5z = 0 Solving -12 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -5z = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5z = 0 + 12 -5z = 0 + 12 Combine like terms: 0 + 12 = 12 -5z = 12 Divide each side by '-5'. z = -2.4 Simplifying z = -2.4Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {-2.4, 1.5}
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