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Simplifying (2z + 1)(2z + -5) = 0 Reorder the terms: (1 + 2z)(2z + -5) = 0 Reorder the terms: (1 + 2z)(-5 + 2z) = 0 Multiply (1 + 2z) * (-5 + 2z) (1(-5 + 2z) + 2z * (-5 + 2z)) = 0 ((-5 * 1 + 2z * 1) + 2z * (-5 + 2z)) = 0 ((-5 + 2z) + 2z * (-5 + 2z)) = 0 (-5 + 2z + (-5 * 2z + 2z * 2z)) = 0 (-5 + 2z + (-10z + 4z2)) = 0 Combine like terms: 2z + -10z = -8z (-5 + -8z + 4z2) = 0 Solving -5 + -8z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -2z)(5 + -2z) = 0Subproblem 1
Set the factor '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 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 = {-0.5, 2.5}
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