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Simplifying 12(4t + -6) + -8(9t + 4) = 0 Reorder the terms: 12(-6 + 4t) + -8(9t + 4) = 0 (-6 * 12 + 4t * 12) + -8(9t + 4) = 0 (-72 + 48t) + -8(9t + 4) = 0 Reorder the terms: -72 + 48t + -8(4 + 9t) = 0 -72 + 48t + (4 * -8 + 9t * -8) = 0 -72 + 48t + (-32 + -72t) = 0 Reorder the terms: -72 + -32 + 48t + -72t = 0 Combine like terms: -72 + -32 = -104 -104 + 48t + -72t = 0 Combine like terms: 48t + -72t = -24t -104 + -24t = 0 Solving -104 + -24t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '104' to each side of the equation. -104 + 104 + -24t = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -24t = 0 + 104 -24t = 0 + 104 Combine like terms: 0 + 104 = 104 -24t = 104 Divide each side by '-24'. t = -4.333333333 Simplifying t = -4.333333333
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