3x-6=1x(7-6x)-14+5x

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Solution for 3x-6=1x(7-6x)-14+5x equation:


Simplifying
3x + -6 = 1x(7 + -6x) + -14 + 5x

Reorder the terms:
-6 + 3x = 1x(7 + -6x) + -14 + 5x
-6 + 3x = (7 * 1x + -6x * 1x) + -14 + 5x
-6 + 3x = (7x + -6x2) + -14 + 5x

Reorder the terms:
-6 + 3x = -14 + 7x + 5x + -6x2

Combine like terms: 7x + 5x = 12x
-6 + 3x = -14 + 12x + -6x2

Solving
-6 + 3x = -14 + 12x + -6x2

Solving for variable 'x'.

Reorder the terms:
-6 + 14 + 3x + -12x + 6x2 = -14 + 12x + -6x2 + 14 + -12x + 6x2

Combine like terms: -6 + 14 = 8
8 + 3x + -12x + 6x2 = -14 + 12x + -6x2 + 14 + -12x + 6x2

Combine like terms: 3x + -12x = -9x
8 + -9x + 6x2 = -14 + 12x + -6x2 + 14 + -12x + 6x2

Reorder the terms:
8 + -9x + 6x2 = -14 + 14 + 12x + -12x + -6x2 + 6x2

Combine like terms: -14 + 14 = 0
8 + -9x + 6x2 = 0 + 12x + -12x + -6x2 + 6x2
8 + -9x + 6x2 = 12x + -12x + -6x2 + 6x2

Combine like terms: 12x + -12x = 0
8 + -9x + 6x2 = 0 + -6x2 + 6x2
8 + -9x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
8 + -9x + 6x2 = 0

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

Divide each side by '6'.
1.333333333 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -1.5x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -1.5x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -1.5x + x2 = 0 + -1.333333333
-1.5x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-1.5x + x2 = -1.333333333

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -1.333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1.333333333 + 0.5625

Combine like terms: -1.333333333 + 0.5625 = -0.770833333
0.5625 + -1.5x + x2 = -0.770833333

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.770833333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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