3x(x-1)=4x+2

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Solution for 3x(x-1)=4x+2 equation:


Simplifying
3x(x + -1) = 4x + 2

Reorder the terms:
3x(-1 + x) = 4x + 2
(-1 * 3x + x * 3x) = 4x + 2
(-3x + 3x2) = 4x + 2

Reorder the terms:
-3x + 3x2 = 2 + 4x

Solving
-3x + 3x2 = 2 + 4x

Solving for variable 'x'.

Reorder the terms:
-2 + -3x + -4x + 3x2 = 2 + 4x + -2 + -4x

Combine like terms: -3x + -4x = -7x
-2 + -7x + 3x2 = 2 + 4x + -2 + -4x

Reorder the terms:
-2 + -7x + 3x2 = 2 + -2 + 4x + -4x

Combine like terms: 2 + -2 = 0
-2 + -7x + 3x2 = 0 + 4x + -4x
-2 + -7x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-2 + -7x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-0.6666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.333333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.333333333x + x2 = 0 + 0.6666666667
-2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.333333333x + x2 = 0.6666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 0.6666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 0.6666666667 + 1.361111112

Combine like terms: 0.6666666667 + 1.361111112 = 2.0277777787
1.361111112 + -2.333333333x + x2 = 2.0277777787

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 2.0277777787

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.424000625 and -1.424000625.

Subproblem 1

x + -1.166666667 = 1.424000625 Simplifying x + -1.166666667 = 1.424000625 Reorder the terms: -1.166666667 + x = 1.424000625 Solving -1.166666667 + x = 1.424000625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.424000625 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.424000625 + 1.166666667 x = 1.424000625 + 1.166666667 Combine like terms: 1.424000625 + 1.166666667 = 2.590667292 x = 2.590667292 Simplifying x = 2.590667292

Subproblem 2

x + -1.166666667 = -1.424000625 Simplifying x + -1.166666667 = -1.424000625 Reorder the terms: -1.166666667 + x = -1.424000625 Solving -1.166666667 + x = -1.424000625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.424000625 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.424000625 + 1.166666667 x = -1.424000625 + 1.166666667 Combine like terms: -1.424000625 + 1.166666667 = -0.257333958 x = -0.257333958 Simplifying x = -0.257333958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.590667292, -0.257333958}

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