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Simplifying (3z + -4)(2 + -1z) = 0 Reorder the terms: (-4 + 3z)(2 + -1z) = 0 Multiply (-4 + 3z) * (2 + -1z) (-4(2 + -1z) + 3z * (2 + -1z)) = 0 ((2 * -4 + -1z * -4) + 3z * (2 + -1z)) = 0 ((-8 + 4z) + 3z * (2 + -1z)) = 0 (-8 + 4z + (2 * 3z + -1z * 3z)) = 0 (-8 + 4z + (6z + -3z2)) = 0 Combine like terms: 4z + 6z = 10z (-8 + 10z + -3z2) = 0 Solving -8 + 10z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + z)(4 + -3z) = 0Subproblem 1
Set the factor '(-2 + z)' equal to zero and attempt to solve: Simplifying -2 + z = 0 Solving -2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0 + 2 z = 0 + 2 Combine like terms: 0 + 2 = 2 z = 2 Simplifying z = 2Subproblem 2
Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 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 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {2, 1.333333333}
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