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Simplifying (3z + 4)(2 + z) = 0 Reorder the terms: (4 + 3z)(2 + z) = 0 Multiply (4 + 3z) * (2 + z) (4(2 + z) + 3z * (2 + z)) = 0 ((2 * 4 + z * 4) + 3z * (2 + z)) = 0 ((8 + 4z) + 3z * (2 + z)) = 0 (8 + 4z + (2 * 3z + z * 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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