3x(2x+1)=5x

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


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

Reorder the terms:
3x(1 + 2x) = 5x
(1 * 3x + 2x * 3x) = 5x
(3x + 6x2) = 5x

Solving
3x + 6x2 = 5x

Solving for variable 'x'.

Reorder the terms:
3x + -5x + 6x2 = 5x + -5x

Combine like terms: 3x + -5x = -2x
-2x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + 3x) = 0

Ignore the factor 2.

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 '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

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

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

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

Divide each side by '3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 0.3333333333}

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