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

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


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

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

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

Remove parenthesis around (-1 + x)
24x + 12x2 = -1 + x

Solving
24x + 12x2 = -1 + x

Solving for variable 'x'.

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

Combine like terms: 24x + -1x = 23x
1 + 23x + 12x2 = -1 + x + 1 + -1x

Reorder the terms:
1 + 23x + 12x2 = -1 + 1 + x + -1x

Combine like terms: -1 + 1 = 0
1 + 23x + 12x2 = 0 + x + -1x
1 + 23x + 12x2 = x + -1x

Combine like terms: x + -1x = 0
1 + 23x + 12x2 = 0

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

Divide each side by '12'.
0.08333333333 + 1.916666667x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + 1.916666667x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + 1.916666667x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + 1.916666667x + x2 = 0 + -0.08333333333
1.916666667x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
1.916666667x + x2 = -0.08333333333

The x term is 1.916666667x.  Take half its coefficient (0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
1.916666667x + 0.9184027781 + x2 = -0.08333333333 + 0.9184027781

Reorder the terms:
0.9184027781 + 1.916666667x + x2 = -0.08333333333 + 0.9184027781

Combine like terms: -0.08333333333 + 0.9184027781 = 0.83506944477
0.9184027781 + 1.916666667x + x2 = 0.83506944477

Factor a perfect square on the left side:
(x + 0.9583333335)(x + 0.9583333335) = 0.83506944477

Calculate the square root of the right side: 0.913821342

Break this problem into two subproblems by setting 
(x + 0.9583333335) equal to 0.913821342 and -0.913821342.

Subproblem 1

x + 0.9583333335 = 0.913821342 Simplifying x + 0.9583333335 = 0.913821342 Reorder the terms: 0.9583333335 + x = 0.913821342 Solving 0.9583333335 + x = 0.913821342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = 0.913821342 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 0.913821342 + -0.9583333335 x = 0.913821342 + -0.9583333335 Combine like terms: 0.913821342 + -0.9583333335 = -0.0445119915 x = -0.0445119915 Simplifying x = -0.0445119915

Subproblem 2

x + 0.9583333335 = -0.913821342 Simplifying x + 0.9583333335 = -0.913821342 Reorder the terms: 0.9583333335 + x = -0.913821342 Solving 0.9583333335 + x = -0.913821342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = -0.913821342 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -0.913821342 + -0.9583333335 x = -0.913821342 + -0.9583333335 Combine like terms: -0.913821342 + -0.9583333335 = -1.8721546755 x = -1.8721546755 Simplifying x = -1.8721546755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.0445119915, -1.8721546755}

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