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Simplifying 5 + 3[2 + -3(2z + 7) + z] = 5z + -4[2z + 3(7 + z) + -8] Reorder the terms: 5 + 3[2 + -3(7 + 2z) + z] = 5z + -4[2z + 3(7 + z) + -8] 5 + 3[2 + (7 * -3 + 2z * -3) + z] = 5z + -4[2z + 3(7 + z) + -8] 5 + 3[2 + (-21 + -6z) + z] = 5z + -4[2z + 3(7 + z) + -8] Combine like terms: 2 + -21 = -19 5 + 3[-19 + -6z + z] = 5z + -4[2z + 3(7 + z) + -8] Combine like terms: -6z + z = -5z 5 + 3[-19 + -5z] = 5z + -4[2z + 3(7 + z) + -8] 5 + [-19 * 3 + -5z * 3] = 5z + -4[2z + 3(7 + z) + -8] 5 + [-57 + -15z] = 5z + -4[2z + 3(7 + z) + -8] Combine like terms: 5 + -57 = -52 -52 + -15z = 5z + -4[2z + 3(7 + z) + -8] -52 + -15z = 5z + -4[2z + (7 * 3 + z * 3) + -8] -52 + -15z = 5z + -4[2z + (21 + 3z) + -8] Reorder the terms: -52 + -15z = 5z + -4[21 + -8 + 2z + 3z] Combine like terms: 21 + -8 = 13 -52 + -15z = 5z + -4[13 + 2z + 3z] Combine like terms: 2z + 3z = 5z -52 + -15z = 5z + -4[13 + 5z] -52 + -15z = 5z + [13 * -4 + 5z * -4] -52 + -15z = 5z + [-52 + -20z] Reorder the terms: -52 + -15z = -52 + 5z + -20z Combine like terms: 5z + -20z = -15z -52 + -15z = -52 + -15z Add '52' to each side of the equation. -52 + 52 + -15z = -52 + 52 + -15z Combine like terms: -52 + 52 = 0 0 + -15z = -52 + 52 + -15z -15z = -52 + 52 + -15z Combine like terms: -52 + 52 = 0 -15z = 0 + -15z -15z = -15z Add '15z' to each side of the equation. -15z + 15z = -15z + 15z Combine like terms: -15z + 15z = 0 0 = -15z + 15z Combine like terms: -15z + 15z = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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