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Simplifying (4z + -11)(z + -2) = 0 Reorder the terms: (-11 + 4z)(z + -2) = 0 Reorder the terms: (-11 + 4z)(-2 + z) = 0 Multiply (-11 + 4z) * (-2 + z) (-11(-2 + z) + 4z * (-2 + z)) = 0 ((-2 * -11 + z * -11) + 4z * (-2 + z)) = 0 ((22 + -11z) + 4z * (-2 + z)) = 0 (22 + -11z + (-2 * 4z + z * 4z)) = 0 (22 + -11z + (-8z + 4z2)) = 0 Combine like terms: -11z + -8z = -19z (22 + -19z + 4z2) = 0 Solving 22 + -19z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(11 + -4z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 2
Set the factor '(11 + -4z)' equal to zero and attempt to solve: Simplifying 11 + -4z = 0 Solving 11 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4z = 0 + -11 -4z = 0 + -11 Combine like terms: 0 + -11 = -11 -4z = -11 Divide each side by '-4'. z = 2.75 Simplifying z = 2.75Solution
z = {2, 2.75}
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