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Simplifying (3z + -4)(3 + z) = 0 Reorder the terms: (-4 + 3z)(3 + z) = 0 Multiply (-4 + 3z) * (3 + z) (-4(3 + z) + 3z * (3 + z)) = 0 ((3 * -4 + z * -4) + 3z * (3 + z)) = 0 ((-12 + -4z) + 3z * (3 + z)) = 0 (-12 + -4z + (3 * 3z + z * 3z)) = 0 (-12 + -4z + (9z + 3z2)) = 0 Combine like terms: -4z + 9z = 5z (-12 + 5z + 3z2) = 0 Solving -12 + 5z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -1z)(4 + -3z) = 0Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 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 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. 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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