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Simplifying 6[3(z + -5) + 14] + -1[3(5z + -4) + 4] = 0 Reorder the terms: 6[3(-5 + z) + 14] + -1[3(5z + -4) + 4] = 0 6[(-5 * 3 + z * 3) + 14] + -1[3(5z + -4) + 4] = 0 6[(-15 + 3z) + 14] + -1[3(5z + -4) + 4] = 0 Reorder the terms: 6[-15 + 14 + 3z] + -1[3(5z + -4) + 4] = 0 Combine like terms: -15 + 14 = -1 6[-1 + 3z] + -1[3(5z + -4) + 4] = 0 [-1 * 6 + 3z * 6] + -1[3(5z + -4) + 4] = 0 [-6 + 18z] + -1[3(5z + -4) + 4] = 0 Reorder the terms: -6 + 18z + -1[3(-4 + 5z) + 4] = 0 -6 + 18z + -1[(-4 * 3 + 5z * 3) + 4] = 0 -6 + 18z + -1[(-12 + 15z) + 4] = 0 Reorder the terms: -6 + 18z + -1[-12 + 4 + 15z] = 0 Combine like terms: -12 + 4 = -8 -6 + 18z + -1[-8 + 15z] = 0 -6 + 18z + [-8 * -1 + 15z * -1] = 0 -6 + 18z + [8 + -15z] = 0 Reorder the terms: -6 + 8 + 18z + -15z = 0 Combine like terms: -6 + 8 = 2 2 + 18z + -15z = 0 Combine like terms: 18z + -15z = 3z 2 + 3z = 0 Solving 2 + 3z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z = 0 + -2 3z = 0 + -2 Combine like terms: 0 + -2 = -2 3z = -2 Divide each side by '3'. z = -0.6666666667 Simplifying z = -0.6666666667
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