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Simplifying (3 + -1z)(3z + -2) = 0 Reorder the terms: (3 + -1z)(-2 + 3z) = 0 Multiply (3 + -1z) * (-2 + 3z) (3(-2 + 3z) + -1z * (-2 + 3z)) = 0 ((-2 * 3 + 3z * 3) + -1z * (-2 + 3z)) = 0 ((-6 + 9z) + -1z * (-2 + 3z)) = 0 (-6 + 9z + (-2 * -1z + 3z * -1z)) = 0 (-6 + 9z + (2z + -3z2)) = 0 Combine like terms: 9z + 2z = 11z (-6 + 11z + -3z2) = 0 Solving -6 + 11z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + z)(2 + -3z) = 0Subproblem 1
Set the factor '(-3 + z)' equal to zero and attempt to solve: Simplifying -3 + z = 0 Solving -3 + z = 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 + z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0 + 3 z = 0 + 3 Combine like terms: 0 + 3 = 3 z = 3 Simplifying z = 3Subproblem 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 = {3, 0.6666666667}
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