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Simplifying 7z(11z + -2)(z + -5) = 0 Reorder the terms: 7z(-2 + 11z)(z + -5) = 0 Reorder the terms: 7z(-2 + 11z)(-5 + z) = 0 Multiply (-2 + 11z) * (-5 + z) 7z(-2(-5 + z) + 11z * (-5 + z)) = 0 7z((-5 * -2 + z * -2) + 11z * (-5 + z)) = 0 7z((10 + -2z) + 11z * (-5 + z)) = 0 7z(10 + -2z + (-5 * 11z + z * 11z)) = 0 7z(10 + -2z + (-55z + 11z2)) = 0 Combine like terms: -2z + -55z = -57z 7z(10 + -57z + 11z2) = 0 (10 * 7z + -57z * 7z + 11z2 * 7z) = 0 (70z + -399z2 + 77z3) = 0 Solving 70z + -399z2 + 77z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '7z'. 7z(10 + -57z + 11z2) = 0 Factor a trinomial. 7z((2 + -11z)(5 + -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 '(2 + -11z)' equal to zero and attempt to solve: Simplifying 2 + -11z = 0 Solving 2 + -11z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -11z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11z = 0 + -2 -11z = 0 + -2 Combine like terms: 0 + -2 = -2 -11z = -2 Divide each side by '-11'. z = 0.1818181818 Simplifying z = 0.1818181818Subproblem 3
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {0, 0.1818181818, 5}
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