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Simplifying 5z2 + -5z + 4 + -1z(3z + 4) = 0 Reorder the terms: 5z2 + -5z + 4 + -1z(4 + 3z) = 0 5z2 + -5z + 4 + (4 * -1z + 3z * -1z) = 0 5z2 + -5z + 4 + (-4z + -3z2) = 0 Reorder the terms: 4 + -5z + -4z + 5z2 + -3z2 = 0 Combine like terms: -5z + -4z = -9z 4 + -9z + 5z2 + -3z2 = 0 Combine like terms: 5z2 + -3z2 = 2z2 4 + -9z + 2z2 = 0 Solving 4 + -9z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -2z)(4 + -1z) = 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 '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {0.5, 4}
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