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Simplifying (2z + -1)(6 + z) = 0 Reorder the terms: (-1 + 2z)(6 + z) = 0 Multiply (-1 + 2z) * (6 + z) (-1(6 + z) + 2z * (6 + z)) = 0 ((6 * -1 + z * -1) + 2z * (6 + z)) = 0 ((-6 + -1z) + 2z * (6 + z)) = 0 (-6 + -1z + (6 * 2z + z * 2z)) = 0 (-6 + -1z + (12z + 2z2)) = 0 Combine like terms: -1z + 12z = 11z (-6 + 11z + 2z2) = 0 Solving -6 + 11z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-6 + -1z)(1 + -2z) = 0Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 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 = {-6, 0.5}
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