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Simplifying 40z2 + 12z + -16 = 0 Reorder the terms: -16 + 12z + 40z2 = 0 Solving -16 + 12z + 40z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 3z + 10z2) = 0 Factor a trinomial. 4((-4 + -5z)(1 + -2z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -5z)' equal to zero and attempt to solve: Simplifying -4 + -5z = 0 Solving -4 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5z = 0 + 4 -5z = 0 + 4 Combine like terms: 0 + 4 = 4 -5z = 4 Divide each side by '-5'. z = -0.8 Simplifying z = -0.8Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Solution
z = {-0.8, 0.5}
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