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Simplifying (x + 7)(x + -3) = x(x + 1) Reorder the terms: (7 + x)(x + -3) = x(x + 1) Reorder the terms: (7 + x)(-3 + x) = x(x + 1) Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = x(x + 1) ((-3 * 7 + x * 7) + x(-3 + x)) = x(x + 1) ((-21 + 7x) + x(-3 + x)) = x(x + 1) (-21 + 7x + (-3 * x + x * x)) = x(x + 1) (-21 + 7x + (-3x + x2)) = x(x + 1) Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = x(x + 1) Reorder the terms: -21 + 4x + x2 = x(1 + x) -21 + 4x + x2 = (1 * x + x * x) -21 + 4x + x2 = (1x + x2) Add '-1x2' to each side of the equation. -21 + 4x + x2 + -1x2 = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + 4x + 0 = 1x + x2 + -1x2 -21 + 4x = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + 4x = 1x + 0 -21 + 4x = 1x Solving -21 + 4x = 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. -21 + 4x + -1x = 1x + -1x Combine like terms: 4x + -1x = 3x -21 + 3x = 1x + -1x Combine like terms: 1x + -1x = 0 -21 + 3x = 0 Add '21' to each side of the equation. -21 + 21 + 3x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3x = 0 + 21 3x = 0 + 21 Combine like terms: 0 + 21 = 21 3x = 21 Divide each side by '3'. x = 7 Simplifying x = 7
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