3x(2x-4)-2=5x-(3-4x)

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Solution for 3x(2x-4)-2=5x-(3-4x) equation:


Simplifying
3x(2x + -4) + -2 = 5x + -1(3 + -4x)

Reorder the terms:
3x(-4 + 2x) + -2 = 5x + -1(3 + -4x)
(-4 * 3x + 2x * 3x) + -2 = 5x + -1(3 + -4x)
(-12x + 6x2) + -2 = 5x + -1(3 + -4x)

Reorder the terms:
-2 + -12x + 6x2 = 5x + -1(3 + -4x)
-2 + -12x + 6x2 = 5x + (3 * -1 + -4x * -1)
-2 + -12x + 6x2 = 5x + (-3 + 4x)

Reorder the terms:
-2 + -12x + 6x2 = -3 + 5x + 4x

Combine like terms: 5x + 4x = 9x
-2 + -12x + 6x2 = -3 + 9x

Solving
-2 + -12x + 6x2 = -3 + 9x

Solving for variable 'x'.

Reorder the terms:
-2 + 3 + -12x + -9x + 6x2 = -3 + 9x + 3 + -9x

Combine like terms: -2 + 3 = 1
1 + -12x + -9x + 6x2 = -3 + 9x + 3 + -9x

Combine like terms: -12x + -9x = -21x
1 + -21x + 6x2 = -3 + 9x + 3 + -9x

Reorder the terms:
1 + -21x + 6x2 = -3 + 3 + 9x + -9x

Combine like terms: -3 + 3 = 0
1 + -21x + 6x2 = 0 + 9x + -9x
1 + -21x + 6x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
1 + -21x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -3.5x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -3.5x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -3.5x + x2 = 0 + -0.1666666667
-3.5x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-3.5x + x2 = -0.1666666667

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -0.1666666667 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -0.1666666667 + 3.0625

Combine like terms: -0.1666666667 + 3.0625 = 2.8958333333
3.0625 + -3.5x + x2 = 2.8958333333

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.8958333333

Calculate the square root of the right side: 1.701714821

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.701714821 and -1.701714821.

Subproblem 1

x + -1.75 = 1.701714821 Simplifying x + -1.75 = 1.701714821 Reorder the terms: -1.75 + x = 1.701714821 Solving -1.75 + x = 1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.701714821 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.701714821 + 1.75 x = 1.701714821 + 1.75 Combine like terms: 1.701714821 + 1.75 = 3.451714821 x = 3.451714821 Simplifying x = 3.451714821

Subproblem 2

x + -1.75 = -1.701714821 Simplifying x + -1.75 = -1.701714821 Reorder the terms: -1.75 + x = -1.701714821 Solving -1.75 + x = -1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.701714821 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.701714821 + 1.75 x = -1.701714821 + 1.75 Combine like terms: -1.701714821 + 1.75 = 0.048285179 x = 0.048285179 Simplifying x = 0.048285179

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.451714821, 0.048285179}

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