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Simplifying (4z + -6)(4 + -1z) = 0 Reorder the terms: (-6 + 4z)(4 + -1z) = 0 Multiply (-6 + 4z) * (4 + -1z) (-6(4 + -1z) + 4z * (4 + -1z)) = 0 ((4 * -6 + -1z * -6) + 4z * (4 + -1z)) = 0 ((-24 + 6z) + 4z * (4 + -1z)) = 0 (-24 + 6z + (4 * 4z + -1z * 4z)) = 0 (-24 + 6z + (16z + -4z2)) = 0 Combine like terms: 6z + 16z = 22z (-24 + 22z + -4z2) = 0 Solving -24 + 22z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 11z + -2z2) = 0 Factor a trinomial. 2((-4 + z)(3 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve: Simplifying -4 + z = 0 Solving -4 + z = 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 + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + z = 0 + 4 z = 0 + 4 Combine like terms: 0 + 4 = 4 z = 4 Simplifying z = 4Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 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 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {4, 1.5}
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