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Simplifying (2x + 5)(18x + -2) = (4x + 1)(9x + 10) Reorder the terms: (5 + 2x)(18x + -2) = (4x + 1)(9x + 10) Reorder the terms: (5 + 2x)(-2 + 18x) = (4x + 1)(9x + 10) Multiply (5 + 2x) * (-2 + 18x) (5(-2 + 18x) + 2x * (-2 + 18x)) = (4x + 1)(9x + 10) ((-2 * 5 + 18x * 5) + 2x * (-2 + 18x)) = (4x + 1)(9x + 10) ((-10 + 90x) + 2x * (-2 + 18x)) = (4x + 1)(9x + 10) (-10 + 90x + (-2 * 2x + 18x * 2x)) = (4x + 1)(9x + 10) (-10 + 90x + (-4x + 36x2)) = (4x + 1)(9x + 10) Combine like terms: 90x + -4x = 86x (-10 + 86x + 36x2) = (4x + 1)(9x + 10) Reorder the terms: -10 + 86x + 36x2 = (1 + 4x)(9x + 10) Reorder the terms: -10 + 86x + 36x2 = (1 + 4x)(10 + 9x) Multiply (1 + 4x) * (10 + 9x) -10 + 86x + 36x2 = (1(10 + 9x) + 4x * (10 + 9x)) -10 + 86x + 36x2 = ((10 * 1 + 9x * 1) + 4x * (10 + 9x)) -10 + 86x + 36x2 = ((10 + 9x) + 4x * (10 + 9x)) -10 + 86x + 36x2 = (10 + 9x + (10 * 4x + 9x * 4x)) -10 + 86x + 36x2 = (10 + 9x + (40x + 36x2)) Combine like terms: 9x + 40x = 49x -10 + 86x + 36x2 = (10 + 49x + 36x2) Add '-36x2' to each side of the equation. -10 + 86x + 36x2 + -36x2 = 10 + 49x + 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -10 + 86x + 0 = 10 + 49x + 36x2 + -36x2 -10 + 86x = 10 + 49x + 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -10 + 86x = 10 + 49x + 0 -10 + 86x = 10 + 49x Solving -10 + 86x = 10 + 49x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49x' to each side of the equation. -10 + 86x + -49x = 10 + 49x + -49x Combine like terms: 86x + -49x = 37x -10 + 37x = 10 + 49x + -49x Combine like terms: 49x + -49x = 0 -10 + 37x = 10 + 0 -10 + 37x = 10 Add '10' to each side of the equation. -10 + 10 + 37x = 10 + 10 Combine like terms: -10 + 10 = 0 0 + 37x = 10 + 10 37x = 10 + 10 Combine like terms: 10 + 10 = 20 37x = 20 Divide each side by '37'. x = 0.5405405405 Simplifying x = 0.5405405405
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