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Simplifying 3z2(-6 + -11z2 + 10z4) = 0 (-6 * 3z2 + -11z2 * 3z2 + 10z4 * 3z2) = 0 (-18z2 + -33z4 + 30z6) = 0 Solving -18z2 + -33z4 + 30z6 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z2'. 3z2(-6 + -11z2 + 10z4) = 0 Factor a trinomial. 3z2((-2 + -5z2)(3 + -2z2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(-2 + -5z2)' equal to zero and attempt to solve: Simplifying -2 + -5z2 = 0 Solving -2 + -5z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5z2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5z2 = 0 + 2 -5z2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5z2 = 2 Divide each side by '-5'. z2 = -0.4 Simplifying z2 = -0.4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -2z2)' equal to zero and attempt to solve: Simplifying 3 + -2z2 = 0 Solving 3 + -2z2 = 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 + -2z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z2 = 0 + -3 -2z2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2z2 = -3 Divide each side by '-2'. z2 = 1.5 Simplifying z2 = 1.5 Take the square root of each side: z = {-1.224744871, 1.224744871}Solution
z = {0, -1.224744871, 1.224744871}
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