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Simplifying 36z6 + -13z4 + z2 = 0 Reorder the terms: z2 + -13z4 + 36z6 = 0 Solving z2 + -13z4 + 36z6 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(1 + -13z2 + 36z4) = 0 Factor a trinomial. z2((1 + -9z2)(1 + -4z2)) = 0 Factor a difference between two squares. z2(((1 + 3z)(1 + -3z))(1 + -4z2)) = 0 Factor a difference between two squares. z2(((1 + 2z)(1 + -2z))(1 + 3z)(1 + -3z)) = 0Subproblem 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 '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Subproblem 3
Set the factor '(1 + -3z)' equal to zero and attempt to solve: Simplifying 1 + -3z = 0 Solving 1 + -3z = 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 + -3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3z = 0 + -1 -3z = 0 + -1 Combine like terms: 0 + -1 = -1 -3z = -1 Divide each side by '-3'. z = 0.3333333333 Simplifying z = 0.3333333333Subproblem 4
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 = -0.5Subproblem 5
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, -0.3333333333, 0.3333333333, -0.5, 0.5}
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