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Simplifying [5x + -1][x + 3] + -1[x + -5][5x + 1] = 40 Reorder the terms: [-1 + 5x][x + 3] + -1[x + -5][5x + 1] = 40 Reorder the terms: [-1 + 5x][3 + x] + -1[x + -5][5x + 1] = 40 Multiply [-1 + 5x] * [3 + x] [-1[3 + x] + 5x * [3 + x]] + -1[x + -5][5x + 1] = 40 [[3 * -1 + x * -1] + 5x * [3 + x]] + -1[x + -5][5x + 1] = 40 [[-3 + -1x] + 5x * [3 + x]] + -1[x + -5][5x + 1] = 40 [-3 + -1x + [3 * 5x + x * 5x]] + -1[x + -5][5x + 1] = 40 [-3 + -1x + [15x + 5x2]] + -1[x + -5][5x + 1] = 40 Combine like terms: -1x + 15x = 14x [-3 + 14x + 5x2] + -1[x + -5][5x + 1] = 40 Reorder the terms: -3 + 14x + 5x2 + -1[-5 + x][5x + 1] = 40 Reorder the terms: -3 + 14x + 5x2 + -1[-5 + x][1 + 5x] = 40 Multiply [-5 + x] * [1 + 5x] -3 + 14x + 5x2 + -1[-5[1 + 5x] + x[1 + 5x]] = 40 -3 + 14x + 5x2 + -1[[1 * -5 + 5x * -5] + x[1 + 5x]] = 40 -3 + 14x + 5x2 + -1[[-5 + -25x] + x[1 + 5x]] = 40 -3 + 14x + 5x2 + -1[-5 + -25x + [1 * x + 5x * x]] = 40 -3 + 14x + 5x2 + -1[-5 + -25x + [1x + 5x2]] = 40 Combine like terms: -25x + 1x = -24x -3 + 14x + 5x2 + -1[-5 + -24x + 5x2] = 40 -3 + 14x + 5x2 + [-5 * -1 + -24x * -1 + 5x2 * -1] = 40 -3 + 14x + 5x2 + [5 + 24x + -5x2] = 40 Reorder the terms: -3 + 5 + 14x + 24x + 5x2 + -5x2 = 40 Combine like terms: -3 + 5 = 2 2 + 14x + 24x + 5x2 + -5x2 = 40 Combine like terms: 14x + 24x = 38x 2 + 38x + 5x2 + -5x2 = 40 Combine like terms: 5x2 + -5x2 = 0 2 + 38x + 0 = 40 2 + 38x = 40 Solving 2 + 38x = 40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 38x = 40 + -2 Combine like terms: 2 + -2 = 0 0 + 38x = 40 + -2 38x = 40 + -2 Combine like terms: 40 + -2 = 38 38x = 38 Divide each side by '38'. x = 1 Simplifying x = 1
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