3(x+5)=2x(x+1)

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Solution for 3(x+5)=2x(x+1) equation: 


Simplifying
3(x + 5) = 2x(x + 1)

Reorder the terms:
3(5 + x) = 2x(x + 1)
(5 * 3 + x * 3) = 2x(x + 1)
(15 + 3x) = 2x(x + 1)

Reorder the terms:
15 + 3x = 2x(1 + x)
15 + 3x = (1 * 2x + x * 2x)
15 + 3x = (2x + 2x2)

Solving
15 + 3x = 2x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -2x = 1x
15 + 1x + -2x2 = 2x + 2x2 + -2x + -2x2

Reorder the terms:
15 + 1x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
15 + 1x + -2x2 = 0 + 2x2 + -2x2
15 + 1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + 1x + -2x2 = 0

Factor a trinomial.
(3 + -1x)(5 + 2x) = 0


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {3, -2.5}

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