(x-7)(x+1)=-16

Solution for (x-7)(x+1)=-16 equation:

Simplifying
(x + -7)(x + 1) = -16

Reorder the terms:
(-7 + x)(x + 1) = -16

Reorder the terms:
(-7 + x)(1 + x) = -16

Multiply (-7 + x) * (1 + x)
(-7(1 + x) + x(1 + x)) = -16
((1 * -7 + x * -7) + x(1 + x)) = -16
((-7 + -7x) + x(1 + x)) = -16
(-7 + -7x + (1 * x + x * x)) = -16
(-7 + -7x + (1x + x2)) = -16

Combine like terms: -7x + 1x = -6x
(-7 + -6x + x2) = -16

Solving
-7 + -6x + x2 = -16

Solving for variable 'x'.

Reorder the terms:
-7 + 16 + -6x + x2 = -16 + 16

Combine like terms: -7 + 16 = 9
9 + -6x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
9 + -6x + x2 = 0

Factor a trinomial.
(3 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}