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Simplifying x(6x + 4) = (2x + 1)(2 + 3x) Reorder the terms: x(4 + 6x) = (2x + 1)(2 + 3x) (4 * x + 6x * x) = (2x + 1)(2 + 3x) (4x + 6x2) = (2x + 1)(2 + 3x) Reorder the terms: 4x + 6x2 = (1 + 2x)(2 + 3x) Multiply (1 + 2x) * (2 + 3x) 4x + 6x2 = (1(2 + 3x) + 2x * (2 + 3x)) 4x + 6x2 = ((2 * 1 + 3x * 1) + 2x * (2 + 3x)) 4x + 6x2 = ((2 + 3x) + 2x * (2 + 3x)) 4x + 6x2 = (2 + 3x + (2 * 2x + 3x * 2x)) 4x + 6x2 = (2 + 3x + (4x + 6x2)) Combine like terms: 3x + 4x = 7x 4x + 6x2 = (2 + 7x + 6x2) Add '-6x2' to each side of the equation. 4x + 6x2 + -6x2 = 2 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 4x + 0 = 2 + 7x + 6x2 + -6x2 4x = 2 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 4x = 2 + 7x + 0 4x = 2 + 7x Solving 4x = 2 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 4x + -7x = 2 + 7x + -7x Combine like terms: 4x + -7x = -3x -3x = 2 + 7x + -7x Combine like terms: 7x + -7x = 0 -3x = 2 + 0 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667
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