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Simplifying (4z + -1)(2z + -2) = 0 Reorder the terms: (-1 + 4z)(2z + -2) = 0 Reorder the terms: (-1 + 4z)(-2 + 2z) = 0 Multiply (-1 + 4z) * (-2 + 2z) (-1(-2 + 2z) + 4z * (-2 + 2z)) = 0 ((-2 * -1 + 2z * -1) + 4z * (-2 + 2z)) = 0 ((2 + -2z) + 4z * (-2 + 2z)) = 0 (2 + -2z + (-2 * 4z + 2z * 4z)) = 0 (2 + -2z + (-8z + 8z2)) = 0 Combine like terms: -2z + -8z = -10z (2 + -10z + 8z2) = 0 Solving 2 + -10z + 8z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -5z + 4z2) = 0 Factor a trinomial. 2((1 + -4z)(1 + -1z)) = 0 Ignore the factor 2.Subproblem 1
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 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {0.25, 1}
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