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Simplifying -2z(3z + 2)(z + -5) = 0 Reorder the terms: -2z(2 + 3z)(z + -5) = 0 Reorder the terms: -2z(2 + 3z)(-5 + z) = 0 Multiply (2 + 3z) * (-5 + z) -2z(2(-5 + z) + 3z * (-5 + z)) = 0 -2z((-5 * 2 + z * 2) + 3z * (-5 + z)) = 0 -2z((-10 + 2z) + 3z * (-5 + z)) = 0 -2z(-10 + 2z + (-5 * 3z + z * 3z)) = 0 -2z(-10 + 2z + (-15z + 3z2)) = 0 Combine like terms: 2z + -15z = -13z -2z(-10 + -13z + 3z2) = 0 (-10 * -2z + -13z * -2z + 3z2 * -2z) = 0 (20z + 26z2 + -6z3) = 0 Solving 20z + 26z2 + -6z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(10 + 13z + -3z2) = 0 Factor a trinomial. 2z((5 + -1z)(2 + 3z)) = 0 Ignore the factor 2.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 '(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 = 5Subproblem 3
Set the factor '(2 + 3z)' equal to zero and attempt to solve: Simplifying 2 + 3z = 0 Solving 2 + 3z = 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 + 3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z = 0 + -2 3z = 0 + -2 Combine like terms: 0 + -2 = -2 3z = -2 Divide each side by '3'. z = -0.6666666667 Simplifying z = -0.6666666667Solution
z = {0, 5, -0.6666666667}
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