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Simplifying -2[z + 3(5 + -1z)] + -5(z + -7) = 0 -2[z + (5 * 3 + -1z * 3)] + -5(z + -7) = 0 -2[z + (15 + -3z)] + -5(z + -7) = 0 Reorder the terms: -2[15 + z + -3z] + -5(z + -7) = 0 Combine like terms: z + -3z = -2z -2[15 + -2z] + -5(z + -7) = 0 [15 * -2 + -2z * -2] + -5(z + -7) = 0 [-30 + 4z] + -5(z + -7) = 0 Reorder the terms: -30 + 4z + -5(-7 + z) = 0 -30 + 4z + (-7 * -5 + z * -5) = 0 -30 + 4z + (35 + -5z) = 0 Reorder the terms: -30 + 35 + 4z + -5z = 0 Combine like terms: -30 + 35 = 5 5 + 4z + -5z = 0 Combine like terms: 4z + -5z = -1z 5 + -1z = 0 Solving 5 + -1z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5
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