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Simplifying 5[z + -1(6z + 18) + 3] = 5(z + 3) Reorder the terms: 5[z + -1(18 + 6z) + 3] = 5(z + 3) 5[z + (18 * -1 + 6z * -1) + 3] = 5(z + 3) 5[z + (-18 + -6z) + 3] = 5(z + 3) Reorder the terms: 5[-18 + 3 + z + -6z] = 5(z + 3) Combine like terms: -18 + 3 = -15 5[-15 + z + -6z] = 5(z + 3) Combine like terms: z + -6z = -5z 5[-15 + -5z] = 5(z + 3) [-15 * 5 + -5z * 5] = 5(z + 3) [-75 + -25z] = 5(z + 3) Reorder the terms: -75 + -25z = 5(3 + z) -75 + -25z = (3 * 5 + z * 5) -75 + -25z = (15 + 5z) Solving -75 + -25z = 15 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -75 + -25z + -5z = 15 + 5z + -5z Combine like terms: -25z + -5z = -30z -75 + -30z = 15 + 5z + -5z Combine like terms: 5z + -5z = 0 -75 + -30z = 15 + 0 -75 + -30z = 15 Add '75' to each side of the equation. -75 + 75 + -30z = 15 + 75 Combine like terms: -75 + 75 = 0 0 + -30z = 15 + 75 -30z = 15 + 75 Combine like terms: 15 + 75 = 90 -30z = 90 Divide each side by '-30'. z = -3 Simplifying z = -3
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