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Simplifying 30z2 + -7z + -20 = 68 Reorder the terms: -20 + -7z + 30z2 = 68 Solving -20 + -7z + 30z2 = 68 Solving for variable 'z'. Reorder the terms: -20 + -68 + -7z + 30z2 = 68 + -68 Combine like terms: -20 + -68 = -88 -88 + -7z + 30z2 = 68 + -68 Combine like terms: 68 + -68 = 0 -88 + -7z + 30z2 = 0 Factor a trinomial. (-8 + -5z)(11 + -6z) = 0Subproblem 1
Set the factor '(-8 + -5z)' equal to zero and attempt to solve: Simplifying -8 + -5z = 0 Solving -8 + -5z = 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 + -5z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5z = 0 + 8 -5z = 0 + 8 Combine like terms: 0 + 8 = 8 -5z = 8 Divide each side by '-5'. z = -1.6 Simplifying z = -1.6Subproblem 2
Set the factor '(11 + -6z)' equal to zero and attempt to solve: Simplifying 11 + -6z = 0 Solving 11 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -6z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -6z = 0 + -11 -6z = 0 + -11 Combine like terms: 0 + -11 = -11 -6z = -11 Divide each side by '-6'. z = 1.833333333 Simplifying z = 1.833333333Solution
z = {-1.6, 1.833333333}
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