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Simplifying (x + 6)(4x + -5) = (3x + -2)(x + 7) Reorder the terms: (6 + x)(4x + -5) = (3x + -2)(x + 7) Reorder the terms: (6 + x)(-5 + 4x) = (3x + -2)(x + 7) Multiply (6 + x) * (-5 + 4x) (6(-5 + 4x) + x(-5 + 4x)) = (3x + -2)(x + 7) ((-5 * 6 + 4x * 6) + x(-5 + 4x)) = (3x + -2)(x + 7) ((-30 + 24x) + x(-5 + 4x)) = (3x + -2)(x + 7) (-30 + 24x + (-5 * x + 4x * x)) = (3x + -2)(x + 7) (-30 + 24x + (-5x + 4x2)) = (3x + -2)(x + 7) Combine like terms: 24x + -5x = 19x (-30 + 19x + 4x2) = (3x + -2)(x + 7) Reorder the terms: -30 + 19x + 4x2 = (-2 + 3x)(x + 7) Reorder the terms: -30 + 19x + 4x2 = (-2 + 3x)(7 + x) Multiply (-2 + 3x) * (7 + x) -30 + 19x + 4x2 = (-2(7 + x) + 3x * (7 + x)) -30 + 19x + 4x2 = ((7 * -2 + x * -2) + 3x * (7 + x)) -30 + 19x + 4x2 = ((-14 + -2x) + 3x * (7 + x)) -30 + 19x + 4x2 = (-14 + -2x + (7 * 3x + x * 3x)) -30 + 19x + 4x2 = (-14 + -2x + (21x + 3x2)) Combine like terms: -2x + 21x = 19x -30 + 19x + 4x2 = (-14 + 19x + 3x2) Add '-19x' to each side of the equation. -30 + 19x + -19x + 4x2 = -14 + 19x + -19x + 3x2 Combine like terms: 19x + -19x = 0 -30 + 0 + 4x2 = -14 + 19x + -19x + 3x2 -30 + 4x2 = -14 + 19x + -19x + 3x2 Combine like terms: 19x + -19x = 0 -30 + 4x2 = -14 + 0 + 3x2 -30 + 4x2 = -14 + 3x2 Solving -30 + 4x2 = -14 + 3x2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x2' to each side of the equation. -30 + 4x2 + -3x2 = -14 + 3x2 + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -30 + 1x2 = -14 + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -30 + 1x2 = -14 + 0 -30 + 1x2 = -14 Add '30' to each side of the equation. -30 + 30 + 1x2 = -14 + 30 Combine like terms: -30 + 30 = 0 0 + 1x2 = -14 + 30 1x2 = -14 + 30 Combine like terms: -14 + 30 = 16 1x2 = 16 Divide each side by '1'. x2 = 16 Simplifying x2 = 16 Take the square root of each side: x = {-4, 4}
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