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Simplifying z4 + 7z3 = 8z2 Reorder the terms: 7z3 + z4 = 8z2 Solving 7z3 + z4 = 8z2 Solving for variable 'z'. Reorder the terms: -8z2 + 7z3 + z4 = 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 -8z2 + 7z3 + z4 = 0 Factor out the Greatest Common Factor (GCF), 'z2'. z2(-8 + 7z + z2) = 0 Factor a trinomial. z2((-8 + -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 '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8Subproblem 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, -8, 1}
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