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Simplifying (27x3 + -54x2 + 36x + -8) + -1(3x + -4)(6x + -5) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: (-8 + 36x + -54x2 + 27x3) + -1(3x + -4)(6x + -5) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Remove parenthesis around (-8 + 36x + -54x2 + 27x3) -8 + 36x + -54x2 + 27x3 + -1(3x + -4)(6x + -5) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: -8 + 36x + -54x2 + 27x3 + -1(-4 + 3x)(6x + -5) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: -8 + 36x + -54x2 + 27x3 + -1(-4 + 3x)(-5 + 6x) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Multiply (-4 + 3x) * (-5 + 6x) -8 + 36x + -54x2 + 27x3 + -1(-4(-5 + 6x) + 3x * (-5 + 6x)) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + -1((-5 * -4 + 6x * -4) + 3x * (-5 + 6x)) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + -1((20 + -24x) + 3x * (-5 + 6x)) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + -1(20 + -24x + (-5 * 3x + 6x * 3x)) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + -1(20 + -24x + (-15x + 18x2)) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Combine like terms: -24x + -15x = -39x -8 + 36x + -54x2 + 27x3 + -1(20 + -39x + 18x2) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + (20 * -1 + -39x * -1 + 18x2 * -1) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) -8 + 36x + -54x2 + 27x3 + (-20 + 39x + -18x2) + -45x2 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: -8 + -20 + 36x + 39x + -54x2 + -18x2 + -45x2 + 27x3 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Combine like terms: -8 + -20 = -28 -28 + 36x + 39x + -54x2 + -18x2 + -45x2 + 27x3 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Combine like terms: 36x + 39x = 75x -28 + 75x + -54x2 + -18x2 + -45x2 + 27x3 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Combine like terms: -54x2 + -18x2 = -72x2 -28 + 75x + -72x2 + -45x2 + 27x3 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Combine like terms: -72x2 + -45x2 = -117x2 -28 + 75x + -117x2 + 27x3 = 9x2(3x + -5) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: -28 + 75x + -117x2 + 27x3 = 9x2(-5 + 3x) + -10(x + 3) + -2(6x + -1)(6x + 1) -28 + 75x + -117x2 + 27x3 = (-5 * 9x2 + 3x * 9x2) + -10(x + 3) + -2(6x + -1)(6x + 1) -28 + 75x + -117x2 + 27x3 = (-45x2 + 27x3) + -10(x + 3) + -2(6x + -1)(6x + 1) Reorder the terms: -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -10(3 + x) + -2(6x + -1)(6x + 1) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + (3 * -10 + x * -10) + -2(6x + -1)(6x + 1) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + (-30 + -10x) + -2(6x + -1)(6x + 1) Reorder the terms: -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + 6x)(6x + 1) Reorder the terms: -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + 6x)(1 + 6x) Multiply (-1 + 6x) * (1 + 6x) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1(1 + 6x) + 6x * (1 + 6x)) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2((1 * -1 + 6x * -1) + 6x * (1 + 6x)) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2((-1 + -6x) + 6x * (1 + 6x)) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + -6x + (1 * 6x + 6x * 6x)) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + -6x + (6x + 36x2)) Combine like terms: -6x + 6x = 0 -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + 0 + 36x2) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + -2(-1 + 36x2) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + (-1 * -2 + 36x2 * -2) -28 + 75x + -117x2 + 27x3 = -45x2 + 27x3 + -30 + -10x + (2 + -72x2) Reorder the terms: -28 + 75x + -117x2 + 27x3 = -30 + 2 + -10x + -45x2 + -72x2 + 27x3 Combine like terms: -30 + 2 = -28 -28 + 75x + -117x2 + 27x3 = -28 + -10x + -45x2 + -72x2 + 27x3 Combine like terms: -45x2 + -72x2 = -117x2 -28 + 75x + -117x2 + 27x3 = -28 + -10x + -117x2 + 27x3 Add '28' to each side of the equation. -28 + 75x + -117x2 + 28 + 27x3 = -28 + -10x + -117x2 + 28 + 27x3 Reorder the terms: -28 + 28 + 75x + -117x2 + 27x3 = -28 + -10x + -117x2 + 28 + 27x3 Combine like terms: -28 + 28 = 0 0 + 75x + -117x2 + 27x3 = -28 + -10x + -117x2 + 28 + 27x3 75x + -117x2 + 27x3 = -28 + -10x + -117x2 + 28 + 27x3 Reorder the terms: 75x + -117x2 + 27x3 = -28 + 28 + -10x + -117x2 + 27x3 Combine like terms: -28 + 28 = 0 75x + -117x2 + 27x3 = 0 + -10x + -117x2 + 27x3 75x + -117x2 + 27x3 = -10x + -117x2 + 27x3 Add '117x2' to each side of the equation. 75x + -117x2 + 117x2 + 27x3 = -10x + -117x2 + 117x2 + 27x3 Combine like terms: -117x2 + 117x2 = 0 75x + 0 + 27x3 = -10x + -117x2 + 117x2 + 27x3 75x + 27x3 = -10x + -117x2 + 117x2 + 27x3 Combine like terms: -117x2 + 117x2 = 0 75x + 27x3 = -10x + 0 + 27x3 75x + 27x3 = -10x + 27x3 Add '-27x3' to each side of the equation. 75x + 27x3 + -27x3 = -10x + 27x3 + -27x3 Combine like terms: 27x3 + -27x3 = 0 75x + 0 = -10x + 27x3 + -27x3 75x = -10x + 27x3 + -27x3 Combine like terms: 27x3 + -27x3 = 0 75x = -10x + 0 75x = -10x Solving 75x = -10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10x' to each side of the equation. 75x + 10x = -10x + 10x Combine like terms: 75x + 10x = 85x 85x = -10x + 10x Combine like terms: -10x + 10x = 0 85x = 0 Divide each side by '85'. x = 0 Simplifying x = 0
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