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Simplifying (x + 2)(x + -3) = (x + -4)(x + 5) Reorder the terms: (2 + x)(x + -3) = (x + -4)(x + 5) Reorder the terms: (2 + x)(-3 + x) = (x + -4)(x + 5) Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = (x + -4)(x + 5) ((-3 * 2 + x * 2) + x(-3 + x)) = (x + -4)(x + 5) ((-6 + 2x) + x(-3 + x)) = (x + -4)(x + 5) (-6 + 2x + (-3 * x + x * x)) = (x + -4)(x + 5) (-6 + 2x + (-3x + x2)) = (x + -4)(x + 5) Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = (x + -4)(x + 5) Reorder the terms: -6 + -1x + x2 = (-4 + x)(x + 5) Reorder the terms: -6 + -1x + x2 = (-4 + x)(5 + x) Multiply (-4 + x) * (5 + x) -6 + -1x + x2 = (-4(5 + x) + x(5 + x)) -6 + -1x + x2 = ((5 * -4 + x * -4) + x(5 + x)) -6 + -1x + x2 = ((-20 + -4x) + x(5 + x)) -6 + -1x + x2 = (-20 + -4x + (5 * x + x * x)) -6 + -1x + x2 = (-20 + -4x + (5x + x2)) Combine like terms: -4x + 5x = 1x -6 + -1x + x2 = (-20 + 1x + x2) Add '-1x2' to each side of the equation. -6 + -1x + x2 + -1x2 = -20 + 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -1x + 0 = -20 + 1x + x2 + -1x2 -6 + -1x = -20 + 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -1x = -20 + 1x + 0 -6 + -1x = -20 + 1x Solving -6 + -1x = -20 + 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. -6 + -1x + -1x = -20 + 1x + -1x Combine like terms: -1x + -1x = -2x -6 + -2x = -20 + 1x + -1x Combine like terms: 1x + -1x = 0 -6 + -2x = -20 + 0 -6 + -2x = -20 Add '6' to each side of the equation. -6 + 6 + -2x = -20 + 6 Combine like terms: -6 + 6 = 0 0 + -2x = -20 + 6 -2x = -20 + 6 Combine like terms: -20 + 6 = -14 -2x = -14 Divide each side by '-2'. x = 7 Simplifying x = 7
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