29x(x+6)=8120

Solution for 29x(x+6)=8120 equation:

Simplifying
29x(x + 6) = 8120

Reorder the terms:
29x(6 + x) = 8120
(6 * 29x + x * 29x) = 8120
(174x + 29x2) = 8120

Solving
174x + 29x2 = 8120

Solving for variable 'x'.

Reorder the terms:
-8120 + 174x + 29x2 = 8120 + -8120

Combine like terms: 8120 + -8120 = 0
-8120 + 174x + 29x2 = 0

Factor out the Greatest Common Factor (GCF), '29'.
29(-280 + 6x + x2) = 0

Factor a trinomial.
29((-20 + -1x)(14 + -1x)) = 0

Ignore the factor 29.
Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-20, 14}