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Simplifying 7 + 3(2t + -4) + -3(4t + 6) + -9 = 0 Reorder the terms: 7 + 3(-4 + 2t) + -3(4t + 6) + -9 = 0 7 + (-4 * 3 + 2t * 3) + -3(4t + 6) + -9 = 0 7 + (-12 + 6t) + -3(4t + 6) + -9 = 0 Reorder the terms: 7 + -12 + 6t + -3(6 + 4t) + -9 = 0 7 + -12 + 6t + (6 * -3 + 4t * -3) + -9 = 0 7 + -12 + 6t + (-18 + -12t) + -9 = 0 Reorder the terms: 7 + -12 + -18 + -9 + 6t + -12t = 0 Combine like terms: 7 + -12 = -5 -5 + -18 + -9 + 6t + -12t = 0 Combine like terms: -5 + -18 = -23 -23 + -9 + 6t + -12t = 0 Combine like terms: -23 + -9 = -32 -32 + 6t + -12t = 0 Combine like terms: 6t + -12t = -6t -32 + -6t = 0 Solving -32 + -6t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -6t = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -6t = 0 + 32 -6t = 0 + 32 Combine like terms: 0 + 32 = 32 -6t = 32 Divide each side by '-6'. t = -5.333333333 Simplifying t = -5.333333333
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