# (x+3)(x-7)=-16

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## Solution for (x+3)(x-7)=-16 equation:

Simplifying (x + 3)(x + -7) = -16 Reorder the terms: (3 + x)(x + -7) = -16 Reorder the terms: (3 + x)(-7 + x) = -16 Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) = -16 ((-7 * 3 + x * 3) + x(-7 + x)) = -16 ((-21 + 3x) + x(-7 + x)) = -16 (-21 + 3x + (-7 * x + x * x)) = -16 (-21 + 3x + (-7x + x^{2})) = -16 Combine like terms: 3x + -7x = -4x (-21 + -4x + x^{2}) = -16 Solving -21 + -4x + x^{2}= -16 Solving for variable 'x'. Reorder the terms: -21 + 16 + -4x + x^{2}= -16 + 16 Combine like terms: -21 + 16 = -5 -5 + -4x + x^{2}= -16 + 16 Combine like terms: -16 + 16 = 0 -5 + -4x + x^{2}= 0 Factor a trinomial. (-1 + -1x)(5 + -1x) = 0## Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1## Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5## Solution

x = {-1, 5}

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