5(x+3)=2(x+6)x

Solution for 5(x+3)=2(x+6)x equation:

Simplifying
5(x + 3) = 2(x + 6) * x

Reorder the terms:
5(3 + x) = 2(x + 6) * x
(3 * 5 + x * 5) = 2(x + 6) * x
(15 + 5x) = 2(x + 6) * x

Reorder the terms:
15 + 5x = 2(6 + x) * x

Reorder the terms for easier multiplication:
15 + 5x = 2x(6 + x)
15 + 5x = (6 * 2x + x * 2x)
15 + 5x = (12x + 2x2)

Solving
15 + 5x = 12x + 2x2

Solving for variable 'x'.

Combine like terms: 5x + -12x = -7x
15 + -7x + -2x2 = 12x + 2x2 + -12x + -2x2

Reorder the terms:
15 + -7x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
15 + -7x + -2x2 = 0 + 2x2 + -2x2
15 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + -7x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(5 + x) = 0

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {1.5, -5}