x(4x+1)=3x

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Solution for x(4x+1)=3x equation: 


Simplifying
x(4x + 1) = 3x

Reorder the terms:
x(1 + 4x) = 3x
(1 * x + 4x * x) = 3x
(1x + 4x2) = 3x

Solving
1x + 4x2 = 3x

Solving for variable 'x'.

Reorder the terms:
1x + -3x + 4x2 = 3x + -3x

Combine like terms: 1x + -3x = -2x
-2x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}

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