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Simplifying (2x + -7)(2x + 3) = (4x + 1)(x + 3) Reorder the terms: (-7 + 2x)(2x + 3) = (4x + 1)(x + 3) Reorder the terms: (-7 + 2x)(3 + 2x) = (4x + 1)(x + 3) Multiply (-7 + 2x) * (3 + 2x) (-7(3 + 2x) + 2x * (3 + 2x)) = (4x + 1)(x + 3) ((3 * -7 + 2x * -7) + 2x * (3 + 2x)) = (4x + 1)(x + 3) ((-21 + -14x) + 2x * (3 + 2x)) = (4x + 1)(x + 3) (-21 + -14x + (3 * 2x + 2x * 2x)) = (4x + 1)(x + 3) (-21 + -14x + (6x + 4x2)) = (4x + 1)(x + 3) Combine like terms: -14x + 6x = -8x (-21 + -8x + 4x2) = (4x + 1)(x + 3) Reorder the terms: -21 + -8x + 4x2 = (1 + 4x)(x + 3) Reorder the terms: -21 + -8x + 4x2 = (1 + 4x)(3 + x) Multiply (1 + 4x) * (3 + x) -21 + -8x + 4x2 = (1(3 + x) + 4x * (3 + x)) -21 + -8x + 4x2 = ((3 * 1 + x * 1) + 4x * (3 + x)) -21 + -8x + 4x2 = ((3 + 1x) + 4x * (3 + x)) -21 + -8x + 4x2 = (3 + 1x + (3 * 4x + x * 4x)) -21 + -8x + 4x2 = (3 + 1x + (12x + 4x2)) Combine like terms: 1x + 12x = 13x -21 + -8x + 4x2 = (3 + 13x + 4x2) Add '-4x2' to each side of the equation. -21 + -8x + 4x2 + -4x2 = 3 + 13x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + -8x + 0 = 3 + 13x + 4x2 + -4x2 -21 + -8x = 3 + 13x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + -8x = 3 + 13x + 0 -21 + -8x = 3 + 13x Solving -21 + -8x = 3 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. -21 + -8x + -13x = 3 + 13x + -13x Combine like terms: -8x + -13x = -21x -21 + -21x = 3 + 13x + -13x Combine like terms: 13x + -13x = 0 -21 + -21x = 3 + 0 -21 + -21x = 3 Add '21' to each side of the equation. -21 + 21 + -21x = 3 + 21 Combine like terms: -21 + 21 = 0 0 + -21x = 3 + 21 -21x = 3 + 21 Combine like terms: 3 + 21 = 24 -21x = 24 Divide each side by '-21'. x = -1.142857143 Simplifying x = -1.142857143
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