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Simplifying 5z2 + -12z + 7 = 0 Reorder the terms: 7 + -12z + 5z2 = 0 Solving 7 + -12z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -1z)(7 + -5z) = 0Subproblem 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 '(7 + -5z)' equal to zero and attempt to solve: Simplifying 7 + -5z = 0 Solving 7 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5z = 0 + -7 -5z = 0 + -7 Combine like terms: 0 + -7 = -7 -5z = -7 Divide each side by '-5'. z = 1.4 Simplifying z = 1.4Solution
z = {1, 1.4}
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