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

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


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

Reorder the terms:
2x + -3(6 + x) = -4x(x + -1)
2x + (6 * -3 + x * -3) = -4x(x + -1)
2x + (-18 + -3x) = -4x(x + -1)

Reorder the terms:
-18 + 2x + -3x = -4x(x + -1)

Combine like terms: 2x + -3x = -1x
-18 + -1x = -4x(x + -1)

Reorder the terms:
-18 + -1x = -4x(-1 + x)
-18 + -1x = (-1 * -4x + x * -4x)
-18 + -1x = (4x + -4x2)

Solving
-18 + -1x = 4x + -4x2

Solving for variable 'x'.

Combine like terms: -1x + -4x = -5x
-18 + -5x + 4x2 = 4x + -4x2 + -4x + 4x2

Reorder the terms:
-18 + -5x + 4x2 = 4x + -4x + -4x2 + 4x2

Combine like terms: 4x + -4x = 0
-18 + -5x + 4x2 = 0 + -4x2 + 4x2
-18 + -5x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-18 + -5x + 4x2 = 0

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

Divide each side by '4'.
-4.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1.25x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1.25x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1.25x + x2 = 0 + 4.5
-1.25x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1.25x + x2 = 4.5

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 4.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 4.5 + 0.390625

Combine like terms: 4.5 + 0.390625 = 4.890625
0.390625 + -1.25x + x2 = 4.890625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 4.890625

Calculate the square root of the right side: 2.211475752

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.211475752 and -2.211475752.

Subproblem 1

x + -0.625 = 2.211475752 Simplifying x + -0.625 = 2.211475752 Reorder the terms: -0.625 + x = 2.211475752 Solving -0.625 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.211475752 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.211475752 + 0.625 x = 2.211475752 + 0.625 Combine like terms: 2.211475752 + 0.625 = 2.836475752 x = 2.836475752 Simplifying x = 2.836475752

Subproblem 2

x + -0.625 = -2.211475752 Simplifying x + -0.625 = -2.211475752 Reorder the terms: -0.625 + x = -2.211475752 Solving -0.625 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.211475752 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.211475752 + 0.625 x = -2.211475752 + 0.625 Combine like terms: -2.211475752 + 0.625 = -1.586475752 x = -1.586475752 Simplifying x = -1.586475752

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.836475752, -1.586475752}

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