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Simplifying 3(5x + -6)(3x + 2) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 Reorder the terms: 3(-6 + 5x)(3x + 2) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 Reorder the terms: 3(-6 + 5x)(2 + 3x) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 Multiply (-6 + 5x) * (2 + 3x) 3(-6(2 + 3x) + 5x * (2 + 3x)) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 3((2 * -6 + 3x * -6) + 5x * (2 + 3x)) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 3((-12 + -18x) + 5x * (2 + 3x)) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 3(-12 + -18x + (2 * 5x + 3x * 5x)) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 3(-12 + -18x + (10x + 15x2)) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 Combine like terms: -18x + 10x = -8x 3(-12 + -8x + 15x2) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 (-12 * 3 + -8x * 3 + 15x2 * 3) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 (-36 + -24x + 45x2) + -6(3x + 4)(x + -1) + -3(9x + 1)(x + -2) = 0 Reorder the terms: -36 + -24x + 45x2 + -6(4 + 3x)(x + -1) + -3(9x + 1)(x + -2) = 0 Reorder the terms: -36 + -24x + 45x2 + -6(4 + 3x)(-1 + x) + -3(9x + 1)(x + -2) = 0 Multiply (4 + 3x) * (-1 + x) -36 + -24x + 45x2 + -6(4(-1 + x) + 3x * (-1 + x)) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + -6((-1 * 4 + x * 4) + 3x * (-1 + x)) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + -6((-4 + 4x) + 3x * (-1 + x)) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + -6(-4 + 4x + (-1 * 3x + x * 3x)) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + -6(-4 + 4x + (-3x + 3x2)) + -3(9x + 1)(x + -2) = 0 Combine like terms: 4x + -3x = 1x -36 + -24x + 45x2 + -6(-4 + 1x + 3x2) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + (-4 * -6 + 1x * -6 + 3x2 * -6) + -3(9x + 1)(x + -2) = 0 -36 + -24x + 45x2 + (24 + -6x + -18x2) + -3(9x + 1)(x + -2) = 0 Reorder the terms: -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(1 + 9x)(x + -2) = 0 Reorder the terms: -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(1 + 9x)(-2 + x) = 0 Multiply (1 + 9x) * (-2 + x) -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(1(-2 + x) + 9x * (-2 + x)) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3((-2 * 1 + x * 1) + 9x * (-2 + x)) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3((-2 + 1x) + 9x * (-2 + x)) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(-2 + 1x + (-2 * 9x + x * 9x)) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(-2 + 1x + (-18x + 9x2)) = 0 Combine like terms: 1x + -18x = -17x -36 + -24x + 45x2 + 24 + -6x + -18x2 + -3(-2 + -17x + 9x2) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + (-2 * -3 + -17x * -3 + 9x2 * -3) = 0 -36 + -24x + 45x2 + 24 + -6x + -18x2 + (6 + 51x + -27x2) = 0 Reorder the terms: -36 + 24 + 6 + -24x + -6x + 51x + 45x2 + -18x2 + -27x2 = 0 Combine like terms: -36 + 24 = -12 -12 + 6 + -24x + -6x + 51x + 45x2 + -18x2 + -27x2 = 0 Combine like terms: -12 + 6 = -6 -6 + -24x + -6x + 51x + 45x2 + -18x2 + -27x2 = 0 Combine like terms: -24x + -6x = -30x -6 + -30x + 51x + 45x2 + -18x2 + -27x2 = 0 Combine like terms: -30x + 51x = 21x -6 + 21x + 45x2 + -18x2 + -27x2 = 0 Combine like terms: 45x2 + -18x2 = 27x2 -6 + 21x + 27x2 + -27x2 = 0 Combine like terms: 27x2 + -27x2 = 0 -6 + 21x + 0 = 0 -6 + 21x = 0 Solving -6 + 21x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 21x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 21x = 0 + 6 21x = 0 + 6 Combine like terms: 0 + 6 = 6 21x = 6 Divide each side by '21'. x = 0.2857142857 Simplifying x = 0.2857142857
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