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Simplifying (3x2 + 4x + 6)(6x + 9) = (3x2 + 3x + 6)(6x + 11) Reorder the terms: (6 + 4x + 3x2)(6x + 9) = (3x2 + 3x + 6)(6x + 11) Reorder the terms: (6 + 4x + 3x2)(9 + 6x) = (3x2 + 3x + 6)(6x + 11) Multiply (6 + 4x + 3x2) * (9 + 6x) (6(9 + 6x) + 4x * (9 + 6x) + 3x2 * (9 + 6x)) = (3x2 + 3x + 6)(6x + 11) ((9 * 6 + 6x * 6) + 4x * (9 + 6x) + 3x2 * (9 + 6x)) = (3x2 + 3x + 6)(6x + 11) ((54 + 36x) + 4x * (9 + 6x) + 3x2 * (9 + 6x)) = (3x2 + 3x + 6)(6x + 11) (54 + 36x + (9 * 4x + 6x * 4x) + 3x2 * (9 + 6x)) = (3x2 + 3x + 6)(6x + 11) (54 + 36x + (36x + 24x2) + 3x2 * (9 + 6x)) = (3x2 + 3x + 6)(6x + 11) (54 + 36x + 36x + 24x2 + (9 * 3x2 + 6x * 3x2)) = (3x2 + 3x + 6)(6x + 11) (54 + 36x + 36x + 24x2 + (27x2 + 18x3)) = (3x2 + 3x + 6)(6x + 11) Combine like terms: 36x + 36x = 72x (54 + 72x + 24x2 + 27x2 + 18x3) = (3x2 + 3x + 6)(6x + 11) Combine like terms: 24x2 + 27x2 = 51x2 (54 + 72x + 51x2 + 18x3) = (3x2 + 3x + 6)(6x + 11) Reorder the terms: 54 + 72x + 51x2 + 18x3 = (6 + 3x + 3x2)(6x + 11) Reorder the terms: 54 + 72x + 51x2 + 18x3 = (6 + 3x + 3x2)(11 + 6x) Multiply (6 + 3x + 3x2) * (11 + 6x) 54 + 72x + 51x2 + 18x3 = (6(11 + 6x) + 3x * (11 + 6x) + 3x2 * (11 + 6x)) 54 + 72x + 51x2 + 18x3 = ((11 * 6 + 6x * 6) + 3x * (11 + 6x) + 3x2 * (11 + 6x)) 54 + 72x + 51x2 + 18x3 = ((66 + 36x) + 3x * (11 + 6x) + 3x2 * (11 + 6x)) 54 + 72x + 51x2 + 18x3 = (66 + 36x + (11 * 3x + 6x * 3x) + 3x2 * (11 + 6x)) 54 + 72x + 51x2 + 18x3 = (66 + 36x + (33x + 18x2) + 3x2 * (11 + 6x)) 54 + 72x + 51x2 + 18x3 = (66 + 36x + 33x + 18x2 + (11 * 3x2 + 6x * 3x2)) 54 + 72x + 51x2 + 18x3 = (66 + 36x + 33x + 18x2 + (33x2 + 18x3)) Combine like terms: 36x + 33x = 69x 54 + 72x + 51x2 + 18x3 = (66 + 69x + 18x2 + 33x2 + 18x3) Combine like terms: 18x2 + 33x2 = 51x2 54 + 72x + 51x2 + 18x3 = (66 + 69x + 51x2 + 18x3) Add '-51x2' to each side of the equation. 54 + 72x + 51x2 + -51x2 + 18x3 = 66 + 69x + 51x2 + -51x2 + 18x3 Combine like terms: 51x2 + -51x2 = 0 54 + 72x + 0 + 18x3 = 66 + 69x + 51x2 + -51x2 + 18x3 54 + 72x + 18x3 = 66 + 69x + 51x2 + -51x2 + 18x3 Combine like terms: 51x2 + -51x2 = 0 54 + 72x + 18x3 = 66 + 69x + 0 + 18x3 54 + 72x + 18x3 = 66 + 69x + 18x3 Add '-18x3' to each side of the equation. 54 + 72x + 18x3 + -18x3 = 66 + 69x + 18x3 + -18x3 Combine like terms: 18x3 + -18x3 = 0 54 + 72x + 0 = 66 + 69x + 18x3 + -18x3 54 + 72x = 66 + 69x + 18x3 + -18x3 Combine like terms: 18x3 + -18x3 = 0 54 + 72x = 66 + 69x + 0 54 + 72x = 66 + 69x Solving 54 + 72x = 66 + 69x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-69x' to each side of the equation. 54 + 72x + -69x = 66 + 69x + -69x Combine like terms: 72x + -69x = 3x 54 + 3x = 66 + 69x + -69x Combine like terms: 69x + -69x = 0 54 + 3x = 66 + 0 54 + 3x = 66 Add '-54' to each side of the equation. 54 + -54 + 3x = 66 + -54 Combine like terms: 54 + -54 = 0 0 + 3x = 66 + -54 3x = 66 + -54 Combine like terms: 66 + -54 = 12 3x = 12 Divide each side by '3'. x = 4 Simplifying x = 4
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