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Simplifying (2x + -7)(3x + 1) = (2x + -5)(3x + 2) Reorder the terms: (-7 + 2x)(3x + 1) = (2x + -5)(3x + 2) Reorder the terms: (-7 + 2x)(1 + 3x) = (2x + -5)(3x + 2) Multiply (-7 + 2x) * (1 + 3x) (-7(1 + 3x) + 2x * (1 + 3x)) = (2x + -5)(3x + 2) ((1 * -7 + 3x * -7) + 2x * (1 + 3x)) = (2x + -5)(3x + 2) ((-7 + -21x) + 2x * (1 + 3x)) = (2x + -5)(3x + 2) (-7 + -21x + (1 * 2x + 3x * 2x)) = (2x + -5)(3x + 2) (-7 + -21x + (2x + 6x2)) = (2x + -5)(3x + 2) Combine like terms: -21x + 2x = -19x (-7 + -19x + 6x2) = (2x + -5)(3x + 2) Reorder the terms: -7 + -19x + 6x2 = (-5 + 2x)(3x + 2) Reorder the terms: -7 + -19x + 6x2 = (-5 + 2x)(2 + 3x) Multiply (-5 + 2x) * (2 + 3x) -7 + -19x + 6x2 = (-5(2 + 3x) + 2x * (2 + 3x)) -7 + -19x + 6x2 = ((2 * -5 + 3x * -5) + 2x * (2 + 3x)) -7 + -19x + 6x2 = ((-10 + -15x) + 2x * (2 + 3x)) -7 + -19x + 6x2 = (-10 + -15x + (2 * 2x + 3x * 2x)) -7 + -19x + 6x2 = (-10 + -15x + (4x + 6x2)) Combine like terms: -15x + 4x = -11x -7 + -19x + 6x2 = (-10 + -11x + 6x2) Add '-6x2' to each side of the equation. -7 + -19x + 6x2 + -6x2 = -10 + -11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -7 + -19x + 0 = -10 + -11x + 6x2 + -6x2 -7 + -19x = -10 + -11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -7 + -19x = -10 + -11x + 0 -7 + -19x = -10 + -11x Solving -7 + -19x = -10 + -11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11x' to each side of the equation. -7 + -19x + 11x = -10 + -11x + 11x Combine like terms: -19x + 11x = -8x -7 + -8x = -10 + -11x + 11x Combine like terms: -11x + 11x = 0 -7 + -8x = -10 + 0 -7 + -8x = -10 Add '7' to each side of the equation. -7 + 7 + -8x = -10 + 7 Combine like terms: -7 + 7 = 0 0 + -8x = -10 + 7 -8x = -10 + 7 Combine like terms: -10 + 7 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375
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