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Simplifying z(5z + -3)(4z + 1) = 0 Reorder the terms: z(-3 + 5z)(4z + 1) = 0 Reorder the terms: z(-3 + 5z)(1 + 4z) = 0 Multiply (-3 + 5z) * (1 + 4z) z(-3(1 + 4z) + 5z * (1 + 4z)) = 0 z((1 * -3 + 4z * -3) + 5z * (1 + 4z)) = 0 z((-3 + -12z) + 5z * (1 + 4z)) = 0 z(-3 + -12z + (1 * 5z + 4z * 5z)) = 0 z(-3 + -12z + (5z + 20z2)) = 0 Combine like terms: -12z + 5z = -7z z(-3 + -7z + 20z2) = 0 (-3 * z + -7z * z + 20z2 * z) = 0 (-3z + -7z2 + 20z3) = 0 Solving -3z + -7z2 + 20z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-3 + -7z + 20z2) = 0 Factor a trinomial. z((-1 + -4z)(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 '(-1 + -4z)' equal to zero and attempt to solve: Simplifying -1 + -4z = 0 Solving -1 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4z = 0 + 1 -4z = 0 + 1 Combine like terms: 0 + 1 = 1 -4z = 1 Divide each side by '-4'. z = -0.25 Simplifying z = -0.25Subproblem 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, -0.25, 0.6}
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