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Simplifying 96z2 + 40z + -84 = 0 Reorder the terms: -84 + 40z + 96z2 = 0 Solving -84 + 40z + 96z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 10z + 24z2) = 0 Factor a trinomial. 4((-7 + -6z)(3 + -4z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -6z)' equal to zero and attempt to solve: Simplifying -7 + -6z = 0 Solving -7 + -6z = 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 + -6z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6z = 0 + 7 -6z = 0 + 7 Combine like terms: 0 + 7 = 7 -6z = 7 Divide each side by '-6'. z = -1.166666667 Simplifying z = -1.166666667Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {-1.166666667, 0.75}
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