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Simplifying 3(5z + -8) + -4(z + 6) = 0 Reorder the terms: 3(-8 + 5z) + -4(z + 6) = 0 (-8 * 3 + 5z * 3) + -4(z + 6) = 0 (-24 + 15z) + -4(z + 6) = 0 Reorder the terms: -24 + 15z + -4(6 + z) = 0 -24 + 15z + (6 * -4 + z * -4) = 0 -24 + 15z + (-24 + -4z) = 0 Reorder the terms: -24 + -24 + 15z + -4z = 0 Combine like terms: -24 + -24 = -48 -48 + 15z + -4z = 0 Combine like terms: 15z + -4z = 11z -48 + 11z = 0 Solving -48 + 11z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + 11z = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 11z = 0 + 48 11z = 0 + 48 Combine like terms: 0 + 48 = 48 11z = 48 Divide each side by '11'. z = 4.363636364 Simplifying z = 4.363636364
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