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Simplifying 2z[2 + -1(5 + -3z)] = -3[8 + -2z(z + -2)] 2z[2 + (5 * -1 + -3z * -1)] = -3[8 + -2z(z + -2)] 2z[2 + (-5 + 3z)] = -3[8 + -2z(z + -2)] Combine like terms: 2 + -5 = -3 2z[-3 + 3z] = -3[8 + -2z(z + -2)] [-3 * 2z + 3z * 2z] = -3[8 + -2z(z + -2)] [-6z + 6z2] = -3[8 + -2z(z + -2)] Reorder the terms: -6z + 6z2 = -3[8 + -2z(-2 + z)] -6z + 6z2 = -3[8 + (-2 * -2z + z * -2z)] -6z + 6z2 = -3[8 + (4z + -2z2)] -6z + 6z2 = [8 * -3 + 4z * -3 + -2z2 * -3] -6z + 6z2 = [-24 + -12z + 6z2] Add '-6z2' to each side of the equation. -6z + 6z2 + -6z2 = -24 + -12z + 6z2 + -6z2 Combine like terms: 6z2 + -6z2 = 0 -6z + 0 = -24 + -12z + 6z2 + -6z2 -6z = -24 + -12z + 6z2 + -6z2 Combine like terms: 6z2 + -6z2 = 0 -6z = -24 + -12z + 0 -6z = -24 + -12z Solving -6z = -24 + -12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12z' to each side of the equation. -6z + 12z = -24 + -12z + 12z Combine like terms: -6z + 12z = 6z 6z = -24 + -12z + 12z Combine like terms: -12z + 12z = 0 6z = -24 + 0 6z = -24 Divide each side by '6'. z = -4 Simplifying z = -4
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