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

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 + x2)) = -16

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) = -16

Solving
-21 + -4x + x2 = -16

Solving for variable 'x'.

Reorder the terms:
-21 + 16 + -4x + x2 = -16 + 16

Combine like terms: -21 + 16 = -5
-5 + -4x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
-5 + -4x + x2 = 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}