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

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


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

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

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

Multiply (-1 + 4x) * (2 + 3x)
(-1(2 + 3x) + 4x * (2 + 3x)) = 4x
((2 * -1 + 3x * -1) + 4x * (2 + 3x)) = 4x
((-2 + -3x) + 4x * (2 + 3x)) = 4x
(-2 + -3x + (2 * 4x + 3x * 4x)) = 4x
(-2 + -3x + (8x + 12x2)) = 4x

Combine like terms: -3x + 8x = 5x
(-2 + 5x + 12x2) = 4x

Solving
-2 + 5x + 12x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-2 + 5x + -4x + 12x2 = 4x + -4x

Combine like terms: 5x + -4x = 1x
-2 + 1x + 12x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-2 + 1x + 12x2 = 0

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

Divide each side by '12'.
-0.1666666667 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.08333333333x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.08333333333x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.08333333333x + x2 = 0 + 0.1666666667
0.08333333333x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.08333333333x + x2 = 0.1666666667

The x term is 0.08333333333x.  Take half its coefficient (0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
0.08333333333x + 0.001736111111 + x2 = 0.1666666667 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333x + x2 = 0.1666666667 + 0.001736111111

Combine like terms: 0.1666666667 + 0.001736111111 = 0.168402777811
0.001736111111 + 0.08333333333x + x2 = 0.168402777811

Factor a perfect square on the left side:
(x + 0.04166666667)(x + 0.04166666667) = 0.168402777811

Calculate the square root of the right side: 0.410369075

Break this problem into two subproblems by setting 
(x + 0.04166666667) equal to 0.410369075 and -0.410369075.

Subproblem 1

x + 0.04166666667 = 0.410369075 Simplifying x + 0.04166666667 = 0.410369075 Reorder the terms: 0.04166666667 + x = 0.410369075 Solving 0.04166666667 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = 0.410369075 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 0.410369075 + -0.04166666667 x = 0.410369075 + -0.04166666667 Combine like terms: 0.410369075 + -0.04166666667 = 0.36870240833 x = 0.36870240833 Simplifying x = 0.36870240833

Subproblem 2

x + 0.04166666667 = -0.410369075 Simplifying x + 0.04166666667 = -0.410369075 Reorder the terms: 0.04166666667 + x = -0.410369075 Solving 0.04166666667 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = -0.410369075 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -0.410369075 + -0.04166666667 x = -0.410369075 + -0.04166666667 Combine like terms: -0.410369075 + -0.04166666667 = -0.45203574167 x = -0.45203574167 Simplifying x = -0.45203574167

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.36870240833, -0.45203574167}

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