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Simplifying (2 + z)(4z + -5) = 0 Reorder the terms: (2 + z)(-5 + 4z) = 0 Multiply (2 + z) * (-5 + 4z) (2(-5 + 4z) + z(-5 + 4z)) = 0 ((-5 * 2 + 4z * 2) + z(-5 + 4z)) = 0 ((-10 + 8z) + z(-5 + 4z)) = 0 (-10 + 8z + (-5 * z + 4z * z)) = 0 (-10 + 8z + (-5z + 4z2)) = 0 Combine like terms: 8z + -5z = 3z (-10 + 3z + 4z2) = 0 Solving -10 + 3z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -1z)(5 + -4z) = 0Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 2
Set the factor '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 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 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25Solution
z = {-2, 1.25}
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