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Simplifying 3x(4x + -1) + -4x(2x + -3) + -1 = 5 + 2x(2x + 3) Reorder the terms: 3x(-1 + 4x) + -4x(2x + -3) + -1 = 5 + 2x(2x + 3) (-1 * 3x + 4x * 3x) + -4x(2x + -3) + -1 = 5 + 2x(2x + 3) (-3x + 12x2) + -4x(2x + -3) + -1 = 5 + 2x(2x + 3) Reorder the terms: -3x + 12x2 + -4x(-3 + 2x) + -1 = 5 + 2x(2x + 3) -3x + 12x2 + (-3 * -4x + 2x * -4x) + -1 = 5 + 2x(2x + 3) -3x + 12x2 + (12x + -8x2) + -1 = 5 + 2x(2x + 3) Reorder the terms: -1 + -3x + 12x + 12x2 + -8x2 = 5 + 2x(2x + 3) Combine like terms: -3x + 12x = 9x -1 + 9x + 12x2 + -8x2 = 5 + 2x(2x + 3) Combine like terms: 12x2 + -8x2 = 4x2 -1 + 9x + 4x2 = 5 + 2x(2x + 3) Reorder the terms: -1 + 9x + 4x2 = 5 + 2x(3 + 2x) -1 + 9x + 4x2 = 5 + (3 * 2x + 2x * 2x) -1 + 9x + 4x2 = 5 + (6x + 4x2) Add '-4x2' to each side of the equation. -1 + 9x + 4x2 + -4x2 = 5 + 6x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -1 + 9x + 0 = 5 + 6x + 4x2 + -4x2 -1 + 9x = 5 + 6x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -1 + 9x = 5 + 6x + 0 -1 + 9x = 5 + 6x Solving -1 + 9x = 5 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. -1 + 9x + -6x = 5 + 6x + -6x Combine like terms: 9x + -6x = 3x -1 + 3x = 5 + 6x + -6x Combine like terms: 6x + -6x = 0 -1 + 3x = 5 + 0 -1 + 3x = 5 Add '1' to each side of the equation. -1 + 1 + 3x = 5 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 5 + 1 3x = 5 + 1 Combine like terms: 5 + 1 = 6 3x = 6 Divide each side by '3'. x = 2 Simplifying x = 2
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