5x(x+1)=x+12

Solution for 5x(x+1)=x+12 equation:

Simplifying
5x(x + 1) = x + 12

Reorder the terms:
5x(1 + x) = x + 12
(1 * 5x + x * 5x) = x + 12
(5x + 5x2) = x + 12

Reorder the terms:
5x + 5x2 = 12 + x

Solving
5x + 5x2 = 12 + x

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + -1x + 5x2 = 12 + x + -12 + -1x

Combine like terms: 5x + -1x = 4x
-12 + 4x + 5x2 = 12 + x + -12 + -1x

Reorder the terms:
-12 + 4x + 5x2 = 12 + -12 + x + -1x

Combine like terms: 12 + -12 = 0
-12 + 4x + 5x2 = 0 + x + -1x
-12 + 4x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 4x + 5x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -5x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-2, 1.2}