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Simplifying (2x + 3)(4x + -7) = (8x + -3)(x + -4) Reorder the terms: (3 + 2x)(4x + -7) = (8x + -3)(x + -4) Reorder the terms: (3 + 2x)(-7 + 4x) = (8x + -3)(x + -4) Multiply (3 + 2x) * (-7 + 4x) (3(-7 + 4x) + 2x * (-7 + 4x)) = (8x + -3)(x + -4) ((-7 * 3 + 4x * 3) + 2x * (-7 + 4x)) = (8x + -3)(x + -4) ((-21 + 12x) + 2x * (-7 + 4x)) = (8x + -3)(x + -4) (-21 + 12x + (-7 * 2x + 4x * 2x)) = (8x + -3)(x + -4) (-21 + 12x + (-14x + 8x2)) = (8x + -3)(x + -4) Combine like terms: 12x + -14x = -2x (-21 + -2x + 8x2) = (8x + -3)(x + -4) Reorder the terms: -21 + -2x + 8x2 = (-3 + 8x)(x + -4) Reorder the terms: -21 + -2x + 8x2 = (-3 + 8x)(-4 + x) Multiply (-3 + 8x) * (-4 + x) -21 + -2x + 8x2 = (-3(-4 + x) + 8x * (-4 + x)) -21 + -2x + 8x2 = ((-4 * -3 + x * -3) + 8x * (-4 + x)) -21 + -2x + 8x2 = ((12 + -3x) + 8x * (-4 + x)) -21 + -2x + 8x2 = (12 + -3x + (-4 * 8x + x * 8x)) -21 + -2x + 8x2 = (12 + -3x + (-32x + 8x2)) Combine like terms: -3x + -32x = -35x -21 + -2x + 8x2 = (12 + -35x + 8x2) Add '-8x2' to each side of the equation. -21 + -2x + 8x2 + -8x2 = 12 + -35x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -21 + -2x + 0 = 12 + -35x + 8x2 + -8x2 -21 + -2x = 12 + -35x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -21 + -2x = 12 + -35x + 0 -21 + -2x = 12 + -35x Solving -21 + -2x = 12 + -35x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35x' to each side of the equation. -21 + -2x + 35x = 12 + -35x + 35x Combine like terms: -2x + 35x = 33x -21 + 33x = 12 + -35x + 35x Combine like terms: -35x + 35x = 0 -21 + 33x = 12 + 0 -21 + 33x = 12 Add '21' to each side of the equation. -21 + 21 + 33x = 12 + 21 Combine like terms: -21 + 21 = 0 0 + 33x = 12 + 21 33x = 12 + 21 Combine like terms: 12 + 21 = 33 33x = 33 Divide each side by '33'. x = 1 Simplifying x = 1
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