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Simplifying t(t + -12) + t(t + 2) + 25 = 2t(t + 5) + -15 Reorder the terms: t(-12 + t) + t(t + 2) + 25 = 2t(t + 5) + -15 (-12 * t + t * t) + t(t + 2) + 25 = 2t(t + 5) + -15 (-12t + t2) + t(t + 2) + 25 = 2t(t + 5) + -15 Reorder the terms: -12t + t2 + t(2 + t) + 25 = 2t(t + 5) + -15 -12t + t2 + (2 * t + t * t) + 25 = 2t(t + 5) + -15 -12t + t2 + (2t + t2) + 25 = 2t(t + 5) + -15 Reorder the terms: 25 + -12t + 2t + t2 + t2 = 2t(t + 5) + -15 Combine like terms: -12t + 2t = -10t 25 + -10t + t2 + t2 = 2t(t + 5) + -15 Combine like terms: t2 + t2 = 2t2 25 + -10t + 2t2 = 2t(t + 5) + -15 Reorder the terms: 25 + -10t + 2t2 = 2t(5 + t) + -15 25 + -10t + 2t2 = (5 * 2t + t * 2t) + -15 25 + -10t + 2t2 = (10t + 2t2) + -15 Reorder the terms: 25 + -10t + 2t2 = -15 + 10t + 2t2 Add '-2t2' to each side of the equation. 25 + -10t + 2t2 + -2t2 = -15 + 10t + 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 25 + -10t + 0 = -15 + 10t + 2t2 + -2t2 25 + -10t = -15 + 10t + 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 25 + -10t = -15 + 10t + 0 25 + -10t = -15 + 10t Solving 25 + -10t = -15 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 25 + -10t + -10t = -15 + 10t + -10t Combine like terms: -10t + -10t = -20t 25 + -20t = -15 + 10t + -10t Combine like terms: 10t + -10t = 0 25 + -20t = -15 + 0 25 + -20t = -15 Add '-25' to each side of the equation. 25 + -25 + -20t = -15 + -25 Combine like terms: 25 + -25 = 0 0 + -20t = -15 + -25 -20t = -15 + -25 Combine like terms: -15 + -25 = -40 -20t = -40 Divide each side by '-20'. t = 2 Simplifying t = 2
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