3(x+1)=x(x+5)

Solution for 3(x+1)=x(x+5) equation:

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

Reorder the terms:
3(1 + x) = x(x + 5)
(1 * 3 + x * 3) = x(x + 5)
(3 + 3x) = x(x + 5)

Reorder the terms:
3 + 3x = x(5 + x)
3 + 3x = (5 * x + x * x)
3 + 3x = (5x + x2)

Solving
3 + 3x = 5x + x2

Solving for variable 'x'.

Combine like terms: 3x + -5x = -2x
3 + -2x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
3 + -2x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
3 + -2x + -1x2 = 0 + x2 + -1x2
3 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -2x + -1x2 = 0

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

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {1, -3}