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Simplifying (2z + -5)(3 + z) = 0 Reorder the terms: (-5 + 2z)(3 + z) = 0 Multiply (-5 + 2z) * (3 + z) (-5(3 + z) + 2z * (3 + z)) = 0 ((3 * -5 + z * -5) + 2z * (3 + z)) = 0 ((-15 + -5z) + 2z * (3 + z)) = 0 (-15 + -5z + (3 * 2z + z * 2z)) = 0 (-15 + -5z + (6z + 2z2)) = 0 Combine like terms: -5z + 6z = 1z (-15 + 1z + 2z2) = 0 Solving -15 + 1z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -1z)(5 + -2z) = 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 '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 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 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {-3, 2.5}
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