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Simplifying (6x + 3)(3x + -5) = (9x + -4)(2x + -7) + 7 Reorder the terms: (3 + 6x)(3x + -5) = (9x + -4)(2x + -7) + 7 Reorder the terms: (3 + 6x)(-5 + 3x) = (9x + -4)(2x + -7) + 7 Multiply (3 + 6x) * (-5 + 3x) (3(-5 + 3x) + 6x * (-5 + 3x)) = (9x + -4)(2x + -7) + 7 ((-5 * 3 + 3x * 3) + 6x * (-5 + 3x)) = (9x + -4)(2x + -7) + 7 ((-15 + 9x) + 6x * (-5 + 3x)) = (9x + -4)(2x + -7) + 7 (-15 + 9x + (-5 * 6x + 3x * 6x)) = (9x + -4)(2x + -7) + 7 (-15 + 9x + (-30x + 18x2)) = (9x + -4)(2x + -7) + 7 Combine like terms: 9x + -30x = -21x (-15 + -21x + 18x2) = (9x + -4)(2x + -7) + 7 Reorder the terms: -15 + -21x + 18x2 = (-4 + 9x)(2x + -7) + 7 Reorder the terms: -15 + -21x + 18x2 = (-4 + 9x)(-7 + 2x) + 7 Multiply (-4 + 9x) * (-7 + 2x) -15 + -21x + 18x2 = (-4(-7 + 2x) + 9x * (-7 + 2x)) + 7 -15 + -21x + 18x2 = ((-7 * -4 + 2x * -4) + 9x * (-7 + 2x)) + 7 -15 + -21x + 18x2 = ((28 + -8x) + 9x * (-7 + 2x)) + 7 -15 + -21x + 18x2 = (28 + -8x + (-7 * 9x + 2x * 9x)) + 7 -15 + -21x + 18x2 = (28 + -8x + (-63x + 18x2)) + 7 Combine like terms: -8x + -63x = -71x -15 + -21x + 18x2 = (28 + -71x + 18x2) + 7 Reorder the terms: -15 + -21x + 18x2 = 28 + 7 + -71x + 18x2 Combine like terms: 28 + 7 = 35 -15 + -21x + 18x2 = 35 + -71x + 18x2 Add '-18x2' to each side of the equation. -15 + -21x + 18x2 + -18x2 = 35 + -71x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -15 + -21x + 0 = 35 + -71x + 18x2 + -18x2 -15 + -21x = 35 + -71x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -15 + -21x = 35 + -71x + 0 -15 + -21x = 35 + -71x Solving -15 + -21x = 35 + -71x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71x' to each side of the equation. -15 + -21x + 71x = 35 + -71x + 71x Combine like terms: -21x + 71x = 50x -15 + 50x = 35 + -71x + 71x Combine like terms: -71x + 71x = 0 -15 + 50x = 35 + 0 -15 + 50x = 35 Add '15' to each side of the equation. -15 + 15 + 50x = 35 + 15 Combine like terms: -15 + 15 = 0 0 + 50x = 35 + 15 50x = 35 + 15 Combine like terms: 35 + 15 = 50 50x = 50 Divide each side by '50'. x = 1 Simplifying x = 1
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