4x(3x+6)=2x-1

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Solution for 4x(3x+6)=2x-1 equation:


Simplifying
4x(3x + 6) = 2x + -1

Reorder the terms:
4x(6 + 3x) = 2x + -1
(6 * 4x + 3x * 4x) = 2x + -1
(24x + 12x2) = 2x + -1

Reorder the terms:
24x + 12x2 = -1 + 2x

Solving
24x + 12x2 = -1 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + 24x + -2x + 12x2 = -1 + 2x + 1 + -2x

Combine like terms: 24x + -2x = 22x
1 + 22x + 12x2 = -1 + 2x + 1 + -2x

Reorder the terms:
1 + 22x + 12x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
1 + 22x + 12x2 = 0 + 2x + -2x
1 + 22x + 12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
1 + 22x + 12x2 = 0

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

Divide each side by '12'.
0.08333333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + 1.833333333x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + 1.833333333x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + 1.833333333x + x2 = 0 + -0.08333333333
1.833333333x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
1.833333333x + x2 = -0.08333333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = -0.08333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = -0.08333333333 + 0.8402777775

Combine like terms: -0.08333333333 + 0.8402777775 = 0.75694444417
0.8402777775 + 1.833333333x + x2 = 0.75694444417

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 0.75694444417

Calculate the square root of the right side: 0.870025542

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 0.870025542 and -0.870025542.

Subproblem 1

x + 0.9166666665 = 0.870025542 Simplifying x + 0.9166666665 = 0.870025542 Reorder the terms: 0.9166666665 + x = 0.870025542 Solving 0.9166666665 + x = 0.870025542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 0.870025542 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 0.870025542 + -0.9166666665 x = 0.870025542 + -0.9166666665 Combine like terms: 0.870025542 + -0.9166666665 = -0.0466411245 x = -0.0466411245 Simplifying x = -0.0466411245

Subproblem 2

x + 0.9166666665 = -0.870025542 Simplifying x + 0.9166666665 = -0.870025542 Reorder the terms: 0.9166666665 + x = -0.870025542 Solving 0.9166666665 + x = -0.870025542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -0.870025542 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -0.870025542 + -0.9166666665 x = -0.870025542 + -0.9166666665 Combine like terms: -0.870025542 + -0.9166666665 = -1.7866922085 x = -1.7866922085 Simplifying x = -1.7866922085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.0466411245, -1.7866922085}

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