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Simplifying 3z4 + -3z3 + -7z3 + 7z2 = 0 Reorder the terms: 7z2 + -3z3 + -7z3 + 3z4 = 0 Combine like terms: -3z3 + -7z3 = -10z3 7z2 + -10z3 + 3z4 = 0 Solving 7z2 + -10z3 + 3z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(7 + -10z + 3z2) = 0 Factor a trinomial. z2((1 + -1z)(7 + -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 + -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 = 1Subproblem 3
Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {0, 1, 2.333333333}
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