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Simplifying (4z + -3)(z + -4) = 0 Reorder the terms: (-3 + 4z)(z + -4) = 0 Reorder the terms: (-3 + 4z)(-4 + z) = 0 Multiply (-3 + 4z) * (-4 + z) (-3(-4 + z) + 4z * (-4 + z)) = 0 ((-4 * -3 + z * -3) + 4z * (-4 + z)) = 0 ((12 + -3z) + 4z * (-4 + z)) = 0 (12 + -3z + (-4 * 4z + z * 4z)) = 0 (12 + -3z + (-16z + 4z2)) = 0 Combine like terms: -3z + -16z = -19z (12 + -19z + 4z2) = 0 Solving 12 + -19z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -4z)(4 + -1z) = 0Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Subproblem 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 = {0.75, 4}
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