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Simplifying 5[u(t) + -1u(t + -1)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Multiply u * t 5[tu + -1u(t + -1)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Reorder the terms: 5[tu + -1u(-1 + t)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 5[tu + (-1 * -1u + t * -1u)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Reorder the terms: 5[tu + (-1tu + 1u)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 5[tu + (-1tu + 1u)] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Combine like terms: tu + -1tu = 0 5[0 + 1u] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 5[1u] + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Remove brackets around [1u] 5 * 1u + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Multiply 5 * 1 5u + -3[u(t + -2) + -1u(t + -4)] + 0[u(t + -4)] = 0 Reorder the terms: 5u + -3[u(-2 + t) + -1u(t + -4)] + 0[u(t + -4)] = 0 5u + -3[(-2 * u + t * u) + -1u(t + -4)] + 0[u(t + -4)] = 0 Reorder the terms: 5u + -3[(tu + -2u) + -1u(t + -4)] + 0[u(t + -4)] = 0 5u + -3[(tu + -2u) + -1u(t + -4)] + 0[u(t + -4)] = 0 Reorder the terms: 5u + -3[tu + -2u + -1u(-4 + t)] + 0[u(t + -4)] = 0 5u + -3[tu + -2u + (-4 * -1u + t * -1u)] + 0[u(t + -4)] = 0 Reorder the terms: 5u + -3[tu + -2u + (-1tu + 4u)] + 0[u(t + -4)] = 0 5u + -3[tu + -2u + (-1tu + 4u)] + 0[u(t + -4)] = 0 Reorder the terms: 5u + -3[tu + -1tu + -2u + 4u] + 0[u(t + -4)] = 0 Combine like terms: tu + -1tu = 0 5u + -3[0 + -2u + 4u] + 0[u(t + -4)] = 0 5u + -3[-2u + 4u] + 0[u(t + -4)] = 0 Combine like terms: -2u + 4u = 2u 5u + -3[2u] + 0[u(t + -4)] = 0 Remove brackets around [2u] 5u + -3 * 2u + 0[u(t + -4)] = 0 Multiply -3 * 2 5u + -6u + 0[u(t + -4)] = 0 Reorder the terms: 5u + -6u + 0[u(-4 + t)] = 0 5u + -6u + 0[(-4 * u + t * u)] = 0 Reorder the terms: 5u + -6u + 0[(tu + -4u)] = 0 5u + -6u + 0[(tu + -4u)] = 0 Anything times zero is zero. 5u + -6u + 0[tu + -4u] = 0 Reorder the terms: 0 + 5u + -6u = 0 Remove the zero: 5u + -6u = 0 Combine like terms: 5u + -6u = -1u -1u = 0 Solving -1u = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Divide each side by '-1'. u = 0 Simplifying u = 0
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