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Simplifying (4x + 3)(x + -5) = (2x + 1)(2x + -7) Reorder the terms: (3 + 4x)(x + -5) = (2x + 1)(2x + -7) Reorder the terms: (3 + 4x)(-5 + x) = (2x + 1)(2x + -7) Multiply (3 + 4x) * (-5 + x) (3(-5 + x) + 4x * (-5 + x)) = (2x + 1)(2x + -7) ((-5 * 3 + x * 3) + 4x * (-5 + x)) = (2x + 1)(2x + -7) ((-15 + 3x) + 4x * (-5 + x)) = (2x + 1)(2x + -7) (-15 + 3x + (-5 * 4x + x * 4x)) = (2x + 1)(2x + -7) (-15 + 3x + (-20x + 4x2)) = (2x + 1)(2x + -7) Combine like terms: 3x + -20x = -17x (-15 + -17x + 4x2) = (2x + 1)(2x + -7) Reorder the terms: -15 + -17x + 4x2 = (1 + 2x)(2x + -7) Reorder the terms: -15 + -17x + 4x2 = (1 + 2x)(-7 + 2x) Multiply (1 + 2x) * (-7 + 2x) -15 + -17x + 4x2 = (1(-7 + 2x) + 2x * (-7 + 2x)) -15 + -17x + 4x2 = ((-7 * 1 + 2x * 1) + 2x * (-7 + 2x)) -15 + -17x + 4x2 = ((-7 + 2x) + 2x * (-7 + 2x)) -15 + -17x + 4x2 = (-7 + 2x + (-7 * 2x + 2x * 2x)) -15 + -17x + 4x2 = (-7 + 2x + (-14x + 4x2)) Combine like terms: 2x + -14x = -12x -15 + -17x + 4x2 = (-7 + -12x + 4x2) Add '-4x2' to each side of the equation. -15 + -17x + 4x2 + -4x2 = -7 + -12x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + -17x + 0 = -7 + -12x + 4x2 + -4x2 -15 + -17x = -7 + -12x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + -17x = -7 + -12x + 0 -15 + -17x = -7 + -12x Solving -15 + -17x = -7 + -12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12x' to each side of the equation. -15 + -17x + 12x = -7 + -12x + 12x Combine like terms: -17x + 12x = -5x -15 + -5x = -7 + -12x + 12x Combine like terms: -12x + 12x = 0 -15 + -5x = -7 + 0 -15 + -5x = -7 Add '15' to each side of the equation. -15 + 15 + -5x = -7 + 15 Combine like terms: -15 + 15 = 0 0 + -5x = -7 + 15 -5x = -7 + 15 Combine like terms: -7 + 15 = 8 -5x = 8 Divide each side by '-5'. x = -1.6 Simplifying x = -1.6
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