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Simplifying x(4x + 3) + 2(x * x + 9) = 6x(x + 2) Reorder the terms: x(3 + 4x) + 2(x * x + 9) = 6x(x + 2) (3 * x + 4x * x) + 2(x * x + 9) = 6x(x + 2) (3x + 4x2) + 2(x * x + 9) = 6x(x + 2) Multiply x * x 3x + 4x2 + 2(x2 + 9) = 6x(x + 2) Reorder the terms: 3x + 4x2 + 2(9 + x2) = 6x(x + 2) 3x + 4x2 + (9 * 2 + x2 * 2) = 6x(x + 2) 3x + 4x2 + (18 + 2x2) = 6x(x + 2) Reorder the terms: 18 + 3x + 4x2 + 2x2 = 6x(x + 2) Combine like terms: 4x2 + 2x2 = 6x2 18 + 3x + 6x2 = 6x(x + 2) Reorder the terms: 18 + 3x + 6x2 = 6x(2 + x) 18 + 3x + 6x2 = (2 * 6x + x * 6x) 18 + 3x + 6x2 = (12x + 6x2) Add '-6x2' to each side of the equation. 18 + 3x + 6x2 + -6x2 = 12x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 18 + 3x + 0 = 12x + 6x2 + -6x2 18 + 3x = 12x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 18 + 3x = 12x + 0 18 + 3x = 12x Solving 18 + 3x = 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. 18 + 3x + -12x = 12x + -12x Combine like terms: 3x + -12x = -9x 18 + -9x = 12x + -12x Combine like terms: 12x + -12x = 0 18 + -9x = 0 Add '-18' to each side of the equation. 18 + -18 + -9x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -9x = 0 + -18 -9x = 0 + -18 Combine like terms: 0 + -18 = -18 -9x = -18 Divide each side by '-9'. x = 2 Simplifying x = 2
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