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Simplifying 2z(z + -2) + 2 = 2z2 + 2[z + -2 + -1(5 + z)] Reorder the terms: 2z(-2 + z) + 2 = 2z2 + 2[z + -2 + -1(5 + z)] (-2 * 2z + z * 2z) + 2 = 2z2 + 2[z + -2 + -1(5 + z)] (-4z + 2z2) + 2 = 2z2 + 2[z + -2 + -1(5 + z)] Reorder the terms: 2 + -4z + 2z2 = 2z2 + 2[z + -2 + -1(5 + z)] 2 + -4z + 2z2 = 2z2 + 2[z + -2 + (5 * -1 + z * -1)] 2 + -4z + 2z2 = 2z2 + 2[z + -2 + (-5 + -1z)] Reorder the terms: 2 + -4z + 2z2 = 2z2 + 2[-2 + -5 + z + -1z] Combine like terms: -2 + -5 = -7 2 + -4z + 2z2 = 2z2 + 2[-7 + z + -1z] Combine like terms: z + -1z = 0 2 + -4z + 2z2 = 2z2 + 2[-7 + 0] 2 + -4z + 2z2 = 2z2 + 2[-7] Multiply 2 * -7 2 + -4z + 2z2 = 2z2 + -14 Reorder the terms: 2 + -4z + 2z2 = -14 + 2z2 Add '-2z2' to each side of the equation. 2 + -4z + 2z2 + -2z2 = -14 + 2z2 + -2z2 Combine like terms: 2z2 + -2z2 = 0 2 + -4z + 0 = -14 + 2z2 + -2z2 2 + -4z = -14 + 2z2 + -2z2 Combine like terms: 2z2 + -2z2 = 0 2 + -4z = -14 + 0 2 + -4z = -14 Solving 2 + -4z = -14 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 + -4z = -14 + -2 Combine like terms: 2 + -2 = 0 0 + -4z = -14 + -2 -4z = -14 + -2 Combine like terms: -14 + -2 = -16 -4z = -16 Divide each side by '-4'. z = 4 Simplifying z = 4
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