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Simplifying x2 + 4x + -45 = (x + -5)(x + -7) Reorder the terms: -45 + 4x + x2 = (x + -5)(x + -7) Reorder the terms: -45 + 4x + x2 = (-5 + x)(x + -7) Reorder the terms: -45 + 4x + x2 = (-5 + x)(-7 + x) Multiply (-5 + x) * (-7 + x) -45 + 4x + x2 = (-5(-7 + x) + x(-7 + x)) -45 + 4x + x2 = ((-7 * -5 + x * -5) + x(-7 + x)) -45 + 4x + x2 = ((35 + -5x) + x(-7 + x)) -45 + 4x + x2 = (35 + -5x + (-7 * x + x * x)) -45 + 4x + x2 = (35 + -5x + (-7x + x2)) Combine like terms: -5x + -7x = -12x -45 + 4x + x2 = (35 + -12x + x2) Add '-1x2' to each side of the equation. -45 + 4x + x2 + -1x2 = 35 + -12x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 4x + 0 = 35 + -12x + x2 + -1x2 -45 + 4x = 35 + -12x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 4x = 35 + -12x + 0 -45 + 4x = 35 + -12x Solving -45 + 4x = 35 + -12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12x' to each side of the equation. -45 + 4x + 12x = 35 + -12x + 12x Combine like terms: 4x + 12x = 16x -45 + 16x = 35 + -12x + 12x Combine like terms: -12x + 12x = 0 -45 + 16x = 35 + 0 -45 + 16x = 35 Add '45' to each side of the equation. -45 + 45 + 16x = 35 + 45 Combine like terms: -45 + 45 = 0 0 + 16x = 35 + 45 16x = 35 + 45 Combine like terms: 35 + 45 = 80 16x = 80 Divide each side by '16'. x = 5 Simplifying x = 5
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