x(x+1)(7)=140

Solution for x(x+1)(7)=140 equation:

Simplifying
x(x + 1)(7) = 140

Reorder the terms:
x(1 + x)(7) = 140

Reorder the terms for easier multiplication:
7x(1 + x) = 140
(1 * 7x + x * 7x) = 140
(7x + 7x2) = 140

Solving
7x + 7x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + 7x + 7x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 7x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-20 + x + x2) = 0

Factor a trinomial.
7((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}