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Simplifying 5z2 + -75z + 70 = 0 Reorder the terms: 70 + -75z + 5z2 = 0 Solving 70 + -75z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(14 + -15z + z2) = 0 Factor a trinomial. 5((1 + -1z)(14 + -1z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 2
Set the factor '(14 + -1z)' equal to zero and attempt to solve: Simplifying 14 + -1z = 0 Solving 14 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1z = 0 + -14 -1z = 0 + -14 Combine like terms: 0 + -14 = -14 -1z = -14 Divide each side by '-1'. z = 14 Simplifying z = 14Solution
z = {1, 14}
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