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Simplifying (3x + -2)(4x + c) = 12x + x + -6 Reorder the terms: (-2 + 3x)(4x + c) = 12x + x + -6 Reorder the terms: (-2 + 3x)(c + 4x) = 12x + x + -6 Multiply (-2 + 3x) * (c + 4x) (-2(c + 4x) + 3x * (c + 4x)) = 12x + x + -6 ((c * -2 + 4x * -2) + 3x * (c + 4x)) = 12x + x + -6 ((-2c + -8x) + 3x * (c + 4x)) = 12x + x + -6 (-2c + -8x + (c * 3x + 4x * 3x)) = 12x + x + -6 (-2c + -8x + (3cx + 12x2)) = 12x + x + -6 Reorder the terms: (-2c + 3cx + -8x + 12x2) = 12x + x + -6 (-2c + 3cx + -8x + 12x2) = 12x + x + -6 Reorder the terms: -2c + 3cx + -8x + 12x2 = -6 + 12x + x Combine like terms: 12x + x = 13x -2c + 3cx + -8x + 12x2 = -6 + 13x Solving -2c + 3cx + -8x + 12x2 = -6 + 13x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '8x' to each side of the equation. -2c + 3cx + -8x + 8x + 12x2 = -6 + 13x + 8x Combine like terms: -8x + 8x = 0 -2c + 3cx + 0 + 12x2 = -6 + 13x + 8x -2c + 3cx + 12x2 = -6 + 13x + 8x Combine like terms: 13x + 8x = 21x -2c + 3cx + 12x2 = -6 + 21x Add '-12x2' to each side of the equation. -2c + 3cx + 12x2 + -12x2 = -6 + 21x + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2c + 3cx + 0 = -6 + 21x + -12x2 -2c + 3cx = -6 + 21x + -12x2 Reorder the terms: 6 + -2c + 3cx + -21x + 12x2 = -6 + 21x + -12x2 + 6 + -21x + 12x2 Reorder the terms: 6 + -2c + 3cx + -21x + 12x2 = -6 + 6 + 21x + -21x + -12x2 + 12x2 Combine like terms: -6 + 6 = 0 6 + -2c + 3cx + -21x + 12x2 = 0 + 21x + -21x + -12x2 + 12x2 6 + -2c + 3cx + -21x + 12x2 = 21x + -21x + -12x2 + 12x2 Combine like terms: 21x + -21x = 0 6 + -2c + 3cx + -21x + 12x2 = 0 + -12x2 + 12x2 6 + -2c + 3cx + -21x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 6 + -2c + 3cx + -21x + 12x2 = 0 The solution to this equation could not be determined.
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