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Simplifying z(4z + -3)(z + 4) = 0 Reorder the terms: z(-3 + 4z)(z + 4) = 0 Reorder the terms: z(-3 + 4z)(4 + z) = 0 Multiply (-3 + 4z) * (4 + z) z(-3(4 + z) + 4z * (4 + z)) = 0 z((4 * -3 + z * -3) + 4z * (4 + z)) = 0 z((-12 + -3z) + 4z * (4 + z)) = 0 z(-12 + -3z + (4 * 4z + z * 4z)) = 0 z(-12 + -3z + (16z + 4z2)) = 0 Combine like terms: -3z + 16z = 13z z(-12 + 13z + 4z2) = 0 (-12 * z + 13z * z + 4z2 * z) = 0 (-12z + 13z2 + 4z3) = 0 Solving -12z + 13z2 + 4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-12 + 13z + 4z2) = 0 Factor a trinomial. z((-4 + -1z)(3 + -4z)) = 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 '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 3
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {0, -4, 0.75}
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