(7x-14)(x+1)=0

Solution for (7x-14)(x+1)=0 equation:

Simplifying
(7x + -14)(x + 1) = 0

Reorder the terms:
(-14 + 7x)(x + 1) = 0

Reorder the terms:
(-14 + 7x)(1 + x) = 0

Multiply (-14 + 7x) * (1 + x)
(-14(1 + x) + 7x * (1 + x)) = 0
((1 * -14 + x * -14) + 7x * (1 + x)) = 0
((-14 + -14x) + 7x * (1 + x)) = 0
(-14 + -14x + (1 * 7x + x * 7x)) = 0
(-14 + -14x + (7x + 7x2)) = 0

Combine like terms: -14x + 7x = -7x
(-14 + -7x + 7x2) = 0

Solving
-14 + -7x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + -1x + x2) = 0

Factor a trinomial.
7((-1 + -1x)(2 + -1x)) = 0

Ignore the factor 7.
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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}