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Simplifying z(5z + -3)(z + 2) = 0 Reorder the terms: z(-3 + 5z)(z + 2) = 0 Reorder the terms: z(-3 + 5z)(2 + z) = 0 Multiply (-3 + 5z) * (2 + z) z(-3(2 + z) + 5z * (2 + z)) = 0 z((2 * -3 + z * -3) + 5z * (2 + z)) = 0 z((-6 + -3z) + 5z * (2 + z)) = 0 z(-6 + -3z + (2 * 5z + z * 5z)) = 0 z(-6 + -3z + (10z + 5z2)) = 0 Combine like terms: -3z + 10z = 7z z(-6 + 7z + 5z2) = 0 (-6 * z + 7z * z + 5z2 * z) = 0 (-6z + 7z2 + 5z3) = 0 Solving -6z + 7z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-6 + 7z + 5z2) = 0 Factor a trinomial. z((-2 + -1z)(3 + -5z)) = 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 '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 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 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 3
Set the factor '(3 + -5z)' equal to zero and attempt to solve: Simplifying 3 + -5z = 0 Solving 3 + -5z = 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 + -5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5z = 0 + -3 -5z = 0 + -3 Combine like terms: 0 + -3 = -3 -5z = -3 Divide each side by '-5'. z = 0.6 Simplifying z = 0.6Solution
z = {0, -2, 0.6}
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