3x(x)=1(4x-1)

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


Simplifying
3x(x) = 1(4x + -1)

Multiply x * x
3x2 = 1(4x + -1)

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

Solving
3x2 = -1 + 4x

Solving for variable 'x'.

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

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

Combine like terms: -1 + 1 = 0
1 + -4x + 3x2 = 0 + 4x + -4x
1 + -4x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -4x + 3x2 = 0

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


Subproblem 1
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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.3333333333, 1}

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