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Simplifying (3z + -4)(3 + -1z) = 0 Reorder the terms: (-4 + 3z)(3 + -1z) = 0 Multiply (-4 + 3z) * (3 + -1z) (-4(3 + -1z) + 3z * (3 + -1z)) = 0 ((3 * -4 + -1z * -4) + 3z * (3 + -1z)) = 0 ((-12 + 4z) + 3z * (3 + -1z)) = 0 (-12 + 4z + (3 * 3z + -1z * 3z)) = 0 (-12 + 4z + (9z + -3z2)) = 0 Combine like terms: 4z + 9z = 13z (-12 + 13z + -3z2) = 0 Solving -12 + 13z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + z)(4 + -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 '(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 = {3, 1.333333333}
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