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Simplifying z(5z + -3)(z + 5) = 0 Reorder the terms: z(-3 + 5z)(z + 5) = 0 Reorder the terms: z(-3 + 5z)(5 + z) = 0 Multiply (-3 + 5z) * (5 + z) z(-3(5 + z) + 5z * (5 + z)) = 0 z((5 * -3 + z * -3) + 5z * (5 + z)) = 0 z((-15 + -3z) + 5z * (5 + z)) = 0 z(-15 + -3z + (5 * 5z + z * 5z)) = 0 z(-15 + -3z + (25z + 5z2)) = 0 Combine like terms: -3z + 25z = 22z z(-15 + 22z + 5z2) = 0 (-15 * z + 22z * z + 5z2 * z) = 0 (-15z + 22z2 + 5z3) = 0 Solving -15z + 22z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-15 + 22z + 5z2) = 0 Factor a trinomial. z((-5 + -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 '(-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 '(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, -5, 0.6}
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