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Simplifying (3x + 1)(4x + -2) = 2 + (2x + 4)(6x + -3) Reorder the terms: (1 + 3x)(4x + -2) = 2 + (2x + 4)(6x + -3) Reorder the terms: (1 + 3x)(-2 + 4x) = 2 + (2x + 4)(6x + -3) Multiply (1 + 3x) * (-2 + 4x) (1(-2 + 4x) + 3x * (-2 + 4x)) = 2 + (2x + 4)(6x + -3) ((-2 * 1 + 4x * 1) + 3x * (-2 + 4x)) = 2 + (2x + 4)(6x + -3) ((-2 + 4x) + 3x * (-2 + 4x)) = 2 + (2x + 4)(6x + -3) (-2 + 4x + (-2 * 3x + 4x * 3x)) = 2 + (2x + 4)(6x + -3) (-2 + 4x + (-6x + 12x2)) = 2 + (2x + 4)(6x + -3) Combine like terms: 4x + -6x = -2x (-2 + -2x + 12x2) = 2 + (2x + 4)(6x + -3) Reorder the terms: -2 + -2x + 12x2 = 2 + (4 + 2x)(6x + -3) Reorder the terms: -2 + -2x + 12x2 = 2 + (4 + 2x)(-3 + 6x) Multiply (4 + 2x) * (-3 + 6x) -2 + -2x + 12x2 = 2 + (4(-3 + 6x) + 2x * (-3 + 6x)) -2 + -2x + 12x2 = 2 + ((-3 * 4 + 6x * 4) + 2x * (-3 + 6x)) -2 + -2x + 12x2 = 2 + ((-12 + 24x) + 2x * (-3 + 6x)) -2 + -2x + 12x2 = 2 + (-12 + 24x + (-3 * 2x + 6x * 2x)) -2 + -2x + 12x2 = 2 + (-12 + 24x + (-6x + 12x2)) Combine like terms: 24x + -6x = 18x -2 + -2x + 12x2 = 2 + (-12 + 18x + 12x2) Combine like terms: 2 + -12 = -10 -2 + -2x + 12x2 = -10 + 18x + 12x2 Add '-12x2' to each side of the equation. -2 + -2x + 12x2 + -12x2 = -10 + 18x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2 + -2x + 0 = -10 + 18x + 12x2 + -12x2 -2 + -2x = -10 + 18x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2 + -2x = -10 + 18x + 0 -2 + -2x = -10 + 18x Solving -2 + -2x = -10 + 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. -2 + -2x + -18x = -10 + 18x + -18x Combine like terms: -2x + -18x = -20x -2 + -20x = -10 + 18x + -18x Combine like terms: 18x + -18x = 0 -2 + -20x = -10 + 0 -2 + -20x = -10 Add '2' to each side of the equation. -2 + 2 + -20x = -10 + 2 Combine like terms: -2 + 2 = 0 0 + -20x = -10 + 2 -20x = -10 + 2 Combine like terms: -10 + 2 = -8 -20x = -8 Divide each side by '-20'. x = 0.4 Simplifying x = 0.4
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