(3x+4)(x-1)+54=0

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Solution for (3x+4)(x-1)+54=0 equation: 


Simplifying
(3x + 4)(x + -1) + 54 = 0

Reorder the terms:
(4 + 3x)(x + -1) + 54 = 0

Reorder the terms:
(4 + 3x)(-1 + x) + 54 = 0

Multiply (4 + 3x) * (-1 + x)
(4(-1 + x) + 3x * (-1 + x)) + 54 = 0
((-1 * 4 + x * 4) + 3x * (-1 + x)) + 54 = 0
((-4 + 4x) + 3x * (-1 + x)) + 54 = 0
(-4 + 4x + (-1 * 3x + x * 3x)) + 54 = 0
(-4 + 4x + (-3x + 3x2)) + 54 = 0

Combine like terms: 4x + -3x = 1x
(-4 + 1x + 3x2) + 54 = 0

Reorder the terms:
-4 + 54 + 1x + 3x2 = 0

Combine like terms: -4 + 54 = 50
50 + 1x + 3x2 = 0

Solving
50 + 1x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
16.66666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + 0.3333333333x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + 0.3333333333x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + -16.66666667
0.3333333333x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
0.3333333333x + x2 = -16.66666667

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -16.66666667 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -16.66666667 + 0.02777777779

Combine like terms: -16.66666667 + 0.02777777779 = -16.63888889221
0.02777777779 + 0.3333333333x + x2 = -16.63888889221

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -16.63888889221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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