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Simplifying (4z + -3)(2 + z) = 0 Reorder the terms: (-3 + 4z)(2 + z) = 0 Multiply (-3 + 4z) * (2 + z) (-3(2 + z) + 4z * (2 + z)) = 0 ((2 * -3 + z * -3) + 4z * (2 + z)) = 0 ((-6 + -3z) + 4z * (2 + z)) = 0 (-6 + -3z + (2 * 4z + z * 4z)) = 0 (-6 + -3z + (8z + 4z2)) = 0 Combine like terms: -3z + 8z = 5z (-6 + 5z + 4z2) = 0 Solving -6 + 5z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -1z)(3 + -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 '(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 = 0.75Solution
z = {-2, 0.75}
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