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Simplifying (4 + -1z)(3z + 2) = 0 Reorder the terms: (4 + -1z)(2 + 3z) = 0 Multiply (4 + -1z) * (2 + 3z) (4(2 + 3z) + -1z * (2 + 3z)) = 0 ((2 * 4 + 3z * 4) + -1z * (2 + 3z)) = 0 ((8 + 12z) + -1z * (2 + 3z)) = 0 (8 + 12z + (2 * -1z + 3z * -1z)) = 0 (8 + 12z + (-2z + -3z2)) = 0 Combine like terms: 12z + -2z = 10z (8 + 10z + -3z2) = 0 Solving 8 + 10z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(2 + 3z) = 0Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Subproblem 2
Set the factor '(2 + 3z)' equal to zero and attempt to solve: Simplifying 2 + 3z = 0 Solving 2 + 3z = 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 + 3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z = 0 + -2 3z = 0 + -2 Combine like terms: 0 + -2 = -2 3z = -2 Divide each side by '3'. z = -0.6666666667 Simplifying z = -0.6666666667Solution
z = {4, -0.6666666667}
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