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Simplifying (3 + -2x)(3x + -5) + -3[10 + -1x(2x + 1)] = 0 Reorder the terms: (3 + -2x)(-5 + 3x) + -3[10 + -1x(2x + 1)] = 0 Multiply (3 + -2x) * (-5 + 3x) (3(-5 + 3x) + -2x * (-5 + 3x)) + -3[10 + -1x(2x + 1)] = 0 ((-5 * 3 + 3x * 3) + -2x * (-5 + 3x)) + -3[10 + -1x(2x + 1)] = 0 ((-15 + 9x) + -2x * (-5 + 3x)) + -3[10 + -1x(2x + 1)] = 0 (-15 + 9x + (-5 * -2x + 3x * -2x)) + -3[10 + -1x(2x + 1)] = 0 (-15 + 9x + (10x + -6x2)) + -3[10 + -1x(2x + 1)] = 0 Combine like terms: 9x + 10x = 19x (-15 + 19x + -6x2) + -3[10 + -1x(2x + 1)] = 0 Reorder the terms: -15 + 19x + -6x2 + -3[10 + -1x(1 + 2x)] = 0 -15 + 19x + -6x2 + -3[10 + (1 * -1x + 2x * -1x)] = 0 -15 + 19x + -6x2 + -3[10 + (-1x + -2x2)] = 0 -15 + 19x + -6x2 + [10 * -3 + -1x * -3 + -2x2 * -3] = 0 -15 + 19x + -6x2 + [-30 + 3x + 6x2] = 0 Reorder the terms: -15 + -30 + 19x + 3x + -6x2 + 6x2 = 0 Combine like terms: -15 + -30 = -45 -45 + 19x + 3x + -6x2 + 6x2 = 0 Combine like terms: 19x + 3x = 22x -45 + 22x + -6x2 + 6x2 = 0 Combine like terms: -6x2 + 6x2 = 0 -45 + 22x + 0 = 0 -45 + 22x = 0 Solving -45 + 22x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + 22x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 22x = 0 + 45 22x = 0 + 45 Combine like terms: 0 + 45 = 45 22x = 45 Divide each side by '22'. x = 2.045454545 Simplifying x = 2.045454545
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