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Simplifying (2z + -5)(z + -4) = 0 Reorder the terms: (-5 + 2z)(z + -4) = 0 Reorder the terms: (-5 + 2z)(-4 + z) = 0 Multiply (-5 + 2z) * (-4 + z) (-5(-4 + z) + 2z * (-4 + z)) = 0 ((-4 * -5 + z * -5) + 2z * (-4 + z)) = 0 ((20 + -5z) + 2z * (-4 + z)) = 0 (20 + -5z + (-4 * 2z + z * 2z)) = 0 (20 + -5z + (-8z + 2z2)) = 0 Combine like terms: -5z + -8z = -13z (20 + -13z + 2z2) = 0 Solving 20 + -13z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -2z)(4 + -1z) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {2.5, 4}
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