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Simplifying 4x + -3(2x + 5)(4 + -18x) = 2x + 4 + 12(3x + -3)(3x + -3) Reorder the terms: 4x + -3(5 + 2x)(4 + -18x) = 2x + 4 + 12(3x + -3)(3x + -3) Multiply (5 + 2x) * (4 + -18x) 4x + -3(5(4 + -18x) + 2x * (4 + -18x)) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + -3((4 * 5 + -18x * 5) + 2x * (4 + -18x)) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + -3((20 + -90x) + 2x * (4 + -18x)) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + -3(20 + -90x + (4 * 2x + -18x * 2x)) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + -3(20 + -90x + (8x + -36x2)) = 2x + 4 + 12(3x + -3)(3x + -3) Combine like terms: -90x + 8x = -82x 4x + -3(20 + -82x + -36x2) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + (20 * -3 + -82x * -3 + -36x2 * -3) = 2x + 4 + 12(3x + -3)(3x + -3) 4x + (-60 + 246x + 108x2) = 2x + 4 + 12(3x + -3)(3x + -3) Reorder the terms: -60 + 4x + 246x + 108x2 = 2x + 4 + 12(3x + -3)(3x + -3) Combine like terms: 4x + 246x = 250x -60 + 250x + 108x2 = 2x + 4 + 12(3x + -3)(3x + -3) Reorder the terms: -60 + 250x + 108x2 = 2x + 4 + 12(-3 + 3x)(3x + -3) Reorder the terms: -60 + 250x + 108x2 = 2x + 4 + 12(-3 + 3x)(-3 + 3x) Multiply (-3 + 3x) * (-3 + 3x) -60 + 250x + 108x2 = 2x + 4 + 12(-3(-3 + 3x) + 3x * (-3 + 3x)) -60 + 250x + 108x2 = 2x + 4 + 12((-3 * -3 + 3x * -3) + 3x * (-3 + 3x)) -60 + 250x + 108x2 = 2x + 4 + 12((9 + -9x) + 3x * (-3 + 3x)) -60 + 250x + 108x2 = 2x + 4 + 12(9 + -9x + (-3 * 3x + 3x * 3x)) -60 + 250x + 108x2 = 2x + 4 + 12(9 + -9x + (-9x + 9x2)) Combine like terms: -9x + -9x = -18x -60 + 250x + 108x2 = 2x + 4 + 12(9 + -18x + 9x2) -60 + 250x + 108x2 = 2x + 4 + (9 * 12 + -18x * 12 + 9x2 * 12) -60 + 250x + 108x2 = 2x + 4 + (108 + -216x + 108x2) Reorder the terms: -60 + 250x + 108x2 = 4 + 108 + 2x + -216x + 108x2 Combine like terms: 4 + 108 = 112 -60 + 250x + 108x2 = 112 + 2x + -216x + 108x2 Combine like terms: 2x + -216x = -214x -60 + 250x + 108x2 = 112 + -214x + 108x2 Add '-108x2' to each side of the equation. -60 + 250x + 108x2 + -108x2 = 112 + -214x + 108x2 + -108x2 Combine like terms: 108x2 + -108x2 = 0 -60 + 250x + 0 = 112 + -214x + 108x2 + -108x2 -60 + 250x = 112 + -214x + 108x2 + -108x2 Combine like terms: 108x2 + -108x2 = 0 -60 + 250x = 112 + -214x + 0 -60 + 250x = 112 + -214x Solving -60 + 250x = 112 + -214x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '214x' to each side of the equation. -60 + 250x + 214x = 112 + -214x + 214x Combine like terms: 250x + 214x = 464x -60 + 464x = 112 + -214x + 214x Combine like terms: -214x + 214x = 0 -60 + 464x = 112 + 0 -60 + 464x = 112 Add '60' to each side of the equation. -60 + 60 + 464x = 112 + 60 Combine like terms: -60 + 60 = 0 0 + 464x = 112 + 60 464x = 112 + 60 Combine like terms: 112 + 60 = 172 464x = 172 Divide each side by '464'. x = 0.3706896552 Simplifying x = 0.3706896552
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