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Simplifying z(6z + -5)(z + 3) = 0 Reorder the terms: z(-5 + 6z)(z + 3) = 0 Reorder the terms: z(-5 + 6z)(3 + z) = 0 Multiply (-5 + 6z) * (3 + z) z(-5(3 + z) + 6z * (3 + z)) = 0 z((3 * -5 + z * -5) + 6z * (3 + z)) = 0 z((-15 + -5z) + 6z * (3 + z)) = 0 z(-15 + -5z + (3 * 6z + z * 6z)) = 0 z(-15 + -5z + (18z + 6z2)) = 0 Combine like terms: -5z + 18z = 13z z(-15 + 13z + 6z2) = 0 (-15 * z + 13z * z + 6z2 * z) = 0 (-15z + 13z2 + 6z3) = 0 Solving -15z + 13z2 + 6z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-15 + 13z + 6z2) = 0 Factor a trinomial. z((-3 + -1z)(5 + -6z)) = 0Subproblem 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 '(-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 = -3Subproblem 3
Set the factor '(5 + -6z)' equal to zero and attempt to solve: Simplifying 5 + -6z = 0 Solving 5 + -6z = 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 + -6z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6z = 0 + -5 -6z = 0 + -5 Combine like terms: 0 + -5 = -5 -6z = -5 Divide each side by '-6'. z = 0.8333333333 Simplifying z = 0.8333333333Solution
z = {0, -3, 0.8333333333}
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