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Simplifying (4z + -2)(3 + -1z) = 0 Reorder the terms: (-2 + 4z)(3 + -1z) = 0 Multiply (-2 + 4z) * (3 + -1z) (-2(3 + -1z) + 4z * (3 + -1z)) = 0 ((3 * -2 + -1z * -2) + 4z * (3 + -1z)) = 0 ((-6 + 2z) + 4z * (3 + -1z)) = 0 (-6 + 2z + (3 * 4z + -1z * 4z)) = 0 (-6 + 2z + (12z + -4z2)) = 0 Combine like terms: 2z + 12z = 14z (-6 + 14z + -4z2) = 0 Solving -6 + 14z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 7z + -2z2) = 0 Factor a trinomial. 2((-3 + z)(1 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + z)' equal to zero and attempt to solve: Simplifying -3 + z = 0 Solving -3 + z = 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 + z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0 + 3 z = 0 + 3 Combine like terms: 0 + 3 = 3 z = 3 Simplifying z = 3Subproblem 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 = 0.5Solution
z = {3, 0.5}
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