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Simplifying 2x(4x + -7) + 3 = (2x + -7)(3x + 4) + 2x^{2}Reorder the terms: 2x(-7 + 4x) + 3 = (2x + -7)(3x + 4) + 2x^{2}(-7 * 2x + 4x * 2x) + 3 = (2x + -7)(3x + 4) + 2x^{2}(-14x + 8x^{2}) + 3 = (2x + -7)(3x + 4) + 2x^{2}Reorder the terms: 3 + -14x + 8x^{2}= (2x + -7)(3x + 4) + 2x^{2}Reorder the terms: 3 + -14x + 8x^{2}= (-7 + 2x)(3x + 4) + 2x^{2}Reorder the terms: 3 + -14x + 8x^{2}= (-7 + 2x)(4 + 3x) + 2x^{2}Multiply (-7 + 2x) * (4 + 3x) 3 + -14x + 8x^{2}= (-7(4 + 3x) + 2x * (4 + 3x)) + 2x^{2}3 + -14x + 8x^{2}= ((4 * -7 + 3x * -7) + 2x * (4 + 3x)) + 2x^{2}3 + -14x + 8x^{2}= ((-28 + -21x) + 2x * (4 + 3x)) + 2x^{2}3 + -14x + 8x^{2}= (-28 + -21x + (4 * 2x + 3x * 2x)) + 2x^{2}3 + -14x + 8x^{2}= (-28 + -21x + (8x + 6x^{2})) + 2x^{2}Combine like terms: -21x + 8x = -13x 3 + -14x + 8x^{2}= (-28 + -13x + 6x^{2}) + 2x^{2}Combine like terms: 6x^{2}+ 2x^{2}= 8x^{2}3 + -14x + 8x^{2}= -28 + -13x + 8x^{2}Add '-8x^{2}' to each side of the equation. 3 + -14x + 8x^{2}+ -8x^{2}= -28 + -13x + 8x^{2}+ -8x^{2}Combine like terms: 8x^{2}+ -8x^{2}= 0 3 + -14x + 0 = -28 + -13x + 8x^{2}+ -8x^{2}3 + -14x = -28 + -13x + 8x^{2}+ -8x^{2}Combine like terms: 8x^{2}+ -8x^{2}= 0 3 + -14x = -28 + -13x + 0 3 + -14x = -28 + -13x Solving 3 + -14x = -28 + -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. 3 + -14x + 13x = -28 + -13x + 13x Combine like terms: -14x + 13x = -1x 3 + -1x = -28 + -13x + 13x Combine like terms: -13x + 13x = 0 3 + -1x = -28 + 0 3 + -1x = -28 Add '-3' to each side of the equation. 3 + -3 + -1x = -28 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = -28 + -3 -1x = -28 + -3 Combine like terms: -28 + -3 = -31 -1x = -31 Divide each side by '-1'. x = 31 Simplifying x = 31

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