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Simplifying 4z(15 + -7z) + -5(2 + -7) = 0 (15 * 4z + -7z * 4z) + -5(2 + -7) = 0 (60z + -28z2) + -5(2 + -7) = 0 Combine like terms: 2 + -7 = -5 60z + -28z2 + -5(-5) = 0 Multiply -5 * -5 60z + -28z2 + 25 = 0 Reorder the terms: 25 + 60z + -28z2 = 0 Solving 25 + 60z + -28z2 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -2z)(5 + 14z) = 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 '(5 + 14z)' equal to zero and attempt to solve: Simplifying 5 + 14z = 0 Solving 5 + 14z = 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 + 14z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 14z = 0 + -5 14z = 0 + -5 Combine like terms: 0 + -5 = -5 14z = -5 Divide each side by '14'. z = -0.3571428571 Simplifying z = -0.3571428571Solution
z = {2.5, -0.3571428571}
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