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Simplifying (5 + -1z)(5z + -2) = 0 Reorder the terms: (5 + -1z)(-2 + 5z) = 0 Multiply (5 + -1z) * (-2 + 5z) (5(-2 + 5z) + -1z * (-2 + 5z)) = 0 ((-2 * 5 + 5z * 5) + -1z * (-2 + 5z)) = 0 ((-10 + 25z) + -1z * (-2 + 5z)) = 0 (-10 + 25z + (-2 * -1z + 5z * -1z)) = 0 (-10 + 25z + (2z + -5z2)) = 0 Combine like terms: 25z + 2z = 27z (-10 + 27z + -5z2) = 0 Solving -10 + 27z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + z)(2 + -5z) = 0Subproblem 1
Set the factor '(-5 + z)' equal to zero and attempt to solve: Simplifying -5 + z = 0 Solving -5 + z = 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 + z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z = 0 + 5 z = 0 + 5 Combine like terms: 0 + 5 = 5 z = 5 Simplifying z = 5Subproblem 2
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 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 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Solution
z = {5, 0.4}
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