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Simplifying 2z(2z + 1)(5z + -4) = 0 Reorder the terms: 2z(1 + 2z)(5z + -4) = 0 Reorder the terms: 2z(1 + 2z)(-4 + 5z) = 0 Multiply (1 + 2z) * (-4 + 5z) 2z(1(-4 + 5z) + 2z * (-4 + 5z)) = 0 2z((-4 * 1 + 5z * 1) + 2z * (-4 + 5z)) = 0 2z((-4 + 5z) + 2z * (-4 + 5z)) = 0 2z(-4 + 5z + (-4 * 2z + 5z * 2z)) = 0 2z(-4 + 5z + (-8z + 10z2)) = 0 Combine like terms: 5z + -8z = -3z 2z(-4 + -3z + 10z2) = 0 (-4 * 2z + -3z * 2z + 10z2 * 2z) = 0 (-8z + -6z2 + 20z3) = 0 Solving -8z + -6z2 + 20z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(-4 + -3z + 10z2) = 0 Factor a trinomial. 2z((-1 + -2z)(4 + -5z)) = 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 '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 3
Set the factor '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 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 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8Solution
z = {0, -0.5, 0.8}
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