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Simplifying z4 + 5z3 = 6z2 Reorder the terms: 5z3 + z4 = 6z2 Solving 5z3 + z4 = 6z2 Solving for variable 'z'. Reorder the terms: -6z2 + 5z3 + z4 = 6z2 + -6z2 Combine like terms: 6z2 + -6z2 = 0 -6z2 + 5z3 + z4 = 0 Factor out the Greatest Common Factor (GCF), 'z2'. z2(-6 + 5z + z2) = 0 Factor a trinomial. z2((-6 + -1z)(1 + -1z)) = 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 '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {0, -6, 1}
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