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Simplifying (4z + -3)(5z + -2) = 0 Reorder the terms: (-3 + 4z)(5z + -2) = 0 Reorder the terms: (-3 + 4z)(-2 + 5z) = 0 Multiply (-3 + 4z) * (-2 + 5z) (-3(-2 + 5z) + 4z * (-2 + 5z)) = 0 ((-2 * -3 + 5z * -3) + 4z * (-2 + 5z)) = 0 ((6 + -15z) + 4z * (-2 + 5z)) = 0 (6 + -15z + (-2 * 4z + 5z * 4z)) = 0 (6 + -15z + (-8z + 20z2)) = 0 Combine like terms: -15z + -8z = -23z (6 + -23z + 20z2) = 0 Solving 6 + -23z + 20z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -5z)(3 + -4z) = 0Subproblem 1
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 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 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Subproblem 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 = {0.4, 0.75}
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