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Simplifying 7z3 + 21z2 = 126z Reorder the terms: 21z2 + 7z3 = 126z Solving 21z2 + 7z3 = 126z Solving for variable 'z'. Reorder the terms: -126z + 21z2 + 7z3 = 126z + -126z Combine like terms: 126z + -126z = 0 -126z + 21z2 + 7z3 = 0 Factor out the Greatest Common Factor (GCF), '7z'. 7z(-18 + 3z + z2) = 0 Factor a trinomial. 7z((-6 + -1z)(3 + -1z)) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 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 '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0, -6, 3}
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