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Simplifying (4z + -3)(5 + z) = 0 Reorder the terms: (-3 + 4z)(5 + z) = 0 Multiply (-3 + 4z) * (5 + z) (-3(5 + z) + 4z * (5 + z)) = 0 ((5 * -3 + z * -3) + 4z * (5 + z)) = 0 ((-15 + -3z) + 4z * (5 + z)) = 0 (-15 + -3z + (5 * 4z + z * 4z)) = 0 (-15 + -3z + (20z + 4z2)) = 0 Combine like terms: -3z + 20z = 17z (-15 + 17z + 4z2) = 0 Solving -15 + 17z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(3 + -4z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {-5, 0.75}
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