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Simplifying 3[z + -1(5z + 10) + 6] = 2(z + 1) Reorder the terms: 3[z + -1(10 + 5z) + 6] = 2(z + 1) 3[z + (10 * -1 + 5z * -1) + 6] = 2(z + 1) 3[z + (-10 + -5z) + 6] = 2(z + 1) Reorder the terms: 3[-10 + 6 + z + -5z] = 2(z + 1) Combine like terms: -10 + 6 = -4 3[-4 + z + -5z] = 2(z + 1) Combine like terms: z + -5z = -4z 3[-4 + -4z] = 2(z + 1) [-4 * 3 + -4z * 3] = 2(z + 1) [-12 + -12z] = 2(z + 1) Reorder the terms: -12 + -12z = 2(1 + z) -12 + -12z = (1 * 2 + z * 2) -12 + -12z = (2 + 2z) Solving -12 + -12z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -12 + -12z + -2z = 2 + 2z + -2z Combine like terms: -12z + -2z = -14z -12 + -14z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -12 + -14z = 2 + 0 -12 + -14z = 2 Add '12' to each side of the equation. -12 + 12 + -14z = 2 + 12 Combine like terms: -12 + 12 = 0 0 + -14z = 2 + 12 -14z = 2 + 12 Combine like terms: 2 + 12 = 14 -14z = 14 Divide each side by '-14'. z = -1 Simplifying z = -1
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