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Simplifying 0 = 0.3 * 4180(t + -20) + 0.1 * 385(t + -400) Reorder the terms: 0 = 0.3 * 4180(-20 + t) + 0.1 * 385(t + -400) Multiply 0.3 * 4180 0 = 1254(-20 + t) + 0.1 * 385(t + -400) 0 = (-20 * 1254 + t * 1254) + 0.1 * 385(t + -400) 0 = (-25080 + 1254t) + 0.1 * 385(t + -400) Reorder the terms: 0 = -25080 + 1254t + 0.1 * 385(-400 + t) Multiply 0.1 * 385 0 = -25080 + 1254t + 38.5(-400 + t) 0 = -25080 + 1254t + (-400 * 38.5 + t * 38.5) 0 = -25080 + 1254t + (-15400 + 38.5t) Reorder the terms: 0 = -25080 + -15400 + 1254t + 38.5t Combine like terms: -25080 + -15400 = -40480 0 = -40480 + 1254t + 38.5t Combine like terms: 1254t + 38.5t = 1292.5t 0 = -40480 + 1292.5t Solving 0 = -40480 + 1292.5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1292.5t' to each side of the equation. 0 + -1292.5t = -40480 + 1292.5t + -1292.5t Remove the zero: -1292.5t = -40480 + 1292.5t + -1292.5t Combine like terms: 1292.5t + -1292.5t = 0.0 -1292.5t = -40480 + 0.0 -1292.5t = -40480 Divide each side by '-1292.5'. t = 31.31914894 Simplifying t = 31.31914894
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