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

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


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

Reorder the terms:
2x(-4 + 3x) + 5 = 3x(x + -4)
(-4 * 2x + 3x * 2x) + 5 = 3x(x + -4)
(-8x + 6x2) + 5 = 3x(x + -4)

Reorder the terms:
5 + -8x + 6x2 = 3x(x + -4)

Reorder the terms:
5 + -8x + 6x2 = 3x(-4 + x)
5 + -8x + 6x2 = (-4 * 3x + x * 3x)
5 + -8x + 6x2 = (-12x + 3x2)

Solving
5 + -8x + 6x2 = -12x + 3x2

Solving for variable 'x'.

Reorder the terms:
5 + -8x + 12x + 6x2 + -3x2 = -12x + 3x2 + 12x + -3x2

Combine like terms: -8x + 12x = 4x
5 + 4x + 6x2 + -3x2 = -12x + 3x2 + 12x + -3x2

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

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

Combine like terms: -12x + 12x = 0
5 + 4x + 3x2 = 0 + 3x2 + -3x2
5 + 4x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
5 + 4x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 1.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + -1.666666667
1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
1.333333333x + x2 = -1.666666667

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + 1.333333333x + x2 = -1.2222222228

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = -1.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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