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Simplifying 4((5(z + -4) + 16) + -1(3(3z + -2) + 3)) = 0 Reorder the terms: 4((5(-4 + z) + 16) + -1(3(3z + -2) + 3)) = 0 4(((-4 * 5 + z * 5) + 16) + -1(3(3z + -2) + 3)) = 0 4(((-20 + 5z) + 16) + -1(3(3z + -2) + 3)) = 0 Reorder the terms: 4((-20 + 16 + 5z) + -1(3(3z + -2) + 3)) = 0 Combine like terms: -20 + 16 = -4 4((-4 + 5z) + -1(3(3z + -2) + 3)) = 0 Remove parenthesis around (-4 + 5z) 4(-4 + 5z + -1(3(3z + -2) + 3)) = 0 Reorder the terms: 4(-4 + 5z + -1(3(-2 + 3z) + 3)) = 0 4(-4 + 5z + -1((-2 * 3 + 3z * 3) + 3)) = 0 4(-4 + 5z + -1((-6 + 9z) + 3)) = 0 Reorder the terms: 4(-4 + 5z + -1(-6 + 3 + 9z)) = 0 Combine like terms: -6 + 3 = -3 4(-4 + 5z + -1(-3 + 9z)) = 0 4(-4 + 5z + (-3 * -1 + 9z * -1)) = 0 4(-4 + 5z + (3 + -9z)) = 0 Reorder the terms: 4(-4 + 3 + 5z + -9z) = 0 Combine like terms: -4 + 3 = -1 4(-1 + 5z + -9z) = 0 Combine like terms: 5z + -9z = -4z 4(-1 + -4z) = 0 (-1 * 4 + -4z * 4) = 0 (-4 + -16z) = 0 Solving -4 + -16z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -16z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -16z = 0 + 4 -16z = 0 + 4 Combine like terms: 0 + 4 = 4 -16z = 4 Divide each side by '-16'. z = -0.25 Simplifying z = -0.25
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