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Simplifying (5x + 7)(3x + -8) = (5x + 4)(3x + -5) Reorder the terms: (7 + 5x)(3x + -8) = (5x + 4)(3x + -5) Reorder the terms: (7 + 5x)(-8 + 3x) = (5x + 4)(3x + -5) Multiply (7 + 5x) * (-8 + 3x) (7(-8 + 3x) + 5x * (-8 + 3x)) = (5x + 4)(3x + -5) ((-8 * 7 + 3x * 7) + 5x * (-8 + 3x)) = (5x + 4)(3x + -5) ((-56 + 21x) + 5x * (-8 + 3x)) = (5x + 4)(3x + -5) (-56 + 21x + (-8 * 5x + 3x * 5x)) = (5x + 4)(3x + -5) (-56 + 21x + (-40x + 15x2)) = (5x + 4)(3x + -5) Combine like terms: 21x + -40x = -19x (-56 + -19x + 15x2) = (5x + 4)(3x + -5) Reorder the terms: -56 + -19x + 15x2 = (4 + 5x)(3x + -5) Reorder the terms: -56 + -19x + 15x2 = (4 + 5x)(-5 + 3x) Multiply (4 + 5x) * (-5 + 3x) -56 + -19x + 15x2 = (4(-5 + 3x) + 5x * (-5 + 3x)) -56 + -19x + 15x2 = ((-5 * 4 + 3x * 4) + 5x * (-5 + 3x)) -56 + -19x + 15x2 = ((-20 + 12x) + 5x * (-5 + 3x)) -56 + -19x + 15x2 = (-20 + 12x + (-5 * 5x + 3x * 5x)) -56 + -19x + 15x2 = (-20 + 12x + (-25x + 15x2)) Combine like terms: 12x + -25x = -13x -56 + -19x + 15x2 = (-20 + -13x + 15x2) Add '-15x2' to each side of the equation. -56 + -19x + 15x2 + -15x2 = -20 + -13x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -56 + -19x + 0 = -20 + -13x + 15x2 + -15x2 -56 + -19x = -20 + -13x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -56 + -19x = -20 + -13x + 0 -56 + -19x = -20 + -13x Solving -56 + -19x = -20 + -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. -56 + -19x + 13x = -20 + -13x + 13x Combine like terms: -19x + 13x = -6x -56 + -6x = -20 + -13x + 13x Combine like terms: -13x + 13x = 0 -56 + -6x = -20 + 0 -56 + -6x = -20 Add '56' to each side of the equation. -56 + 56 + -6x = -20 + 56 Combine like terms: -56 + 56 = 0 0 + -6x = -20 + 56 -6x = -20 + 56 Combine like terms: -20 + 56 = 36 -6x = 36 Divide each side by '-6'. x = -6 Simplifying x = -6
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