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Simplifying (x + -3)(4x + 5) = (2x + -6)(2x + -1) Reorder the terms: (-3 + x)(4x + 5) = (2x + -6)(2x + -1) Reorder the terms: (-3 + x)(5 + 4x) = (2x + -6)(2x + -1) Multiply (-3 + x) * (5 + 4x) (-3(5 + 4x) + x(5 + 4x)) = (2x + -6)(2x + -1) ((5 * -3 + 4x * -3) + x(5 + 4x)) = (2x + -6)(2x + -1) ((-15 + -12x) + x(5 + 4x)) = (2x + -6)(2x + -1) (-15 + -12x + (5 * x + 4x * x)) = (2x + -6)(2x + -1) (-15 + -12x + (5x + 4x2)) = (2x + -6)(2x + -1) Combine like terms: -12x + 5x = -7x (-15 + -7x + 4x2) = (2x + -6)(2x + -1) Reorder the terms: -15 + -7x + 4x2 = (-6 + 2x)(2x + -1) Reorder the terms: -15 + -7x + 4x2 = (-6 + 2x)(-1 + 2x) Multiply (-6 + 2x) * (-1 + 2x) -15 + -7x + 4x2 = (-6(-1 + 2x) + 2x * (-1 + 2x)) -15 + -7x + 4x2 = ((-1 * -6 + 2x * -6) + 2x * (-1 + 2x)) -15 + -7x + 4x2 = ((6 + -12x) + 2x * (-1 + 2x)) -15 + -7x + 4x2 = (6 + -12x + (-1 * 2x + 2x * 2x)) -15 + -7x + 4x2 = (6 + -12x + (-2x + 4x2)) Combine like terms: -12x + -2x = -14x -15 + -7x + 4x2 = (6 + -14x + 4x2) Add '-4x2' to each side of the equation. -15 + -7x + 4x2 + -4x2 = 6 + -14x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + -7x + 0 = 6 + -14x + 4x2 + -4x2 -15 + -7x = 6 + -14x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + -7x = 6 + -14x + 0 -15 + -7x = 6 + -14x Solving -15 + -7x = 6 + -14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14x' to each side of the equation. -15 + -7x + 14x = 6 + -14x + 14x Combine like terms: -7x + 14x = 7x -15 + 7x = 6 + -14x + 14x Combine like terms: -14x + 14x = 0 -15 + 7x = 6 + 0 -15 + 7x = 6 Add '15' to each side of the equation. -15 + 15 + 7x = 6 + 15 Combine like terms: -15 + 15 = 0 0 + 7x = 6 + 15 7x = 6 + 15 Combine like terms: 6 + 15 = 21 7x = 21 Divide each side by '7'. x = 3 Simplifying x = 3
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