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Simplifying 3[z + -1(9z + 21) + 5] = 5(z + 2) Reorder the terms: 3[z + -1(21 + 9z) + 5] = 5(z + 2) 3[z + (21 * -1 + 9z * -1) + 5] = 5(z + 2) 3[z + (-21 + -9z) + 5] = 5(z + 2) Reorder the terms: 3[-21 + 5 + z + -9z] = 5(z + 2) Combine like terms: -21 + 5 = -16 3[-16 + z + -9z] = 5(z + 2) Combine like terms: z + -9z = -8z 3[-16 + -8z] = 5(z + 2) [-16 * 3 + -8z * 3] = 5(z + 2) [-48 + -24z] = 5(z + 2) Reorder the terms: -48 + -24z = 5(2 + z) -48 + -24z = (2 * 5 + z * 5) -48 + -24z = (10 + 5z) Solving -48 + -24z = 10 + 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. -48 + -24z + -5z = 10 + 5z + -5z Combine like terms: -24z + -5z = -29z -48 + -29z = 10 + 5z + -5z Combine like terms: 5z + -5z = 0 -48 + -29z = 10 + 0 -48 + -29z = 10 Add '48' to each side of the equation. -48 + 48 + -29z = 10 + 48 Combine like terms: -48 + 48 = 0 0 + -29z = 10 + 48 -29z = 10 + 48 Combine like terms: 10 + 48 = 58 -29z = 58 Divide each side by '-29'. z = -2 Simplifying z = -2
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