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

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

Simplifying
3x2 = 2x(x + 5)

Reorder the terms:
3x2 = 2x(5 + x)
3x2 = (5 * 2x + x * 2x)
3x2 = (10x + 2x2)

Solving
3x2 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10x + 3x2 + -2x2 = 10x + 2x2 + -10x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-10x + 1x2 = 10x + 2x2 + -10x + -2x2

Reorder the terms:
-10x + 1x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-10x + 1x2 = 0 + 2x2 + -2x2
-10x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, 10}