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Simplifying x(3x + 5) = x(x + 9) + 2x(x + 4) + x + 130 Reorder the terms: x(5 + 3x) = x(x + 9) + 2x(x + 4) + x + 130 (5 * x + 3x * x) = x(x + 9) + 2x(x + 4) + x + 130 (5x + 3x2) = x(x + 9) + 2x(x + 4) + x + 130 Reorder the terms: 5x + 3x2 = x(9 + x) + 2x(x + 4) + x + 130 5x + 3x2 = (9 * x + x * x) + 2x(x + 4) + x + 130 5x + 3x2 = (9x + x2) + 2x(x + 4) + x + 130 Reorder the terms: 5x + 3x2 = 9x + x2 + 2x(4 + x) + x + 130 5x + 3x2 = 9x + x2 + (4 * 2x + x * 2x) + x + 130 5x + 3x2 = 9x + x2 + (8x + 2x2) + x + 130 Reorder the terms: 5x + 3x2 = 130 + 9x + 8x + x + x2 + 2x2 Combine like terms: 9x + 8x = 17x 5x + 3x2 = 130 + 17x + x + x2 + 2x2 Combine like terms: 17x + x = 18x 5x + 3x2 = 130 + 18x + x2 + 2x2 Combine like terms: x2 + 2x2 = 3x2 5x + 3x2 = 130 + 18x + 3x2 Add '-3x2' to each side of the equation. 5x + 3x2 + -3x2 = 130 + 18x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5x + 0 = 130 + 18x + 3x2 + -3x2 5x = 130 + 18x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5x = 130 + 18x + 0 5x = 130 + 18x Solving 5x = 130 + 18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18x' to each side of the equation. 5x + -18x = 130 + 18x + -18x Combine like terms: 5x + -18x = -13x -13x = 130 + 18x + -18x Combine like terms: 18x + -18x = 0 -13x = 130 + 0 -13x = 130 Divide each side by '-13'. x = -10 Simplifying x = -10
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