(x-7)(3x+1)+84=

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Solution for (x-7)(3x+1)+84= equation: 


Simplifying
(x + -7)(3x + 1) + 84 = 0

Reorder the terms:
(-7 + x)(3x + 1) + 84 = 0

Reorder the terms:
(-7 + x)(1 + 3x) + 84 = 0

Multiply (-7 + x) * (1 + 3x)
(-7(1 + 3x) + x(1 + 3x)) + 84 = 0
((1 * -7 + 3x * -7) + x(1 + 3x)) + 84 = 0
((-7 + -21x) + x(1 + 3x)) + 84 = 0
(-7 + -21x + (1 * x + 3x * x)) + 84 = 0
(-7 + -21x + (1x + 3x2)) + 84 = 0

Combine like terms: -21x + 1x = -20x
(-7 + -20x + 3x2) + 84 = 0

Reorder the terms:
-7 + 84 + -20x + 3x2 = 0

Combine like terms: -7 + 84 = 77
77 + -20x + 3x2 = 0

Solving
77 + -20x + 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'.
25.66666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-25.66666667' to each side of the equation.
25.66666667 + -6.666666667x + -25.66666667 + x2 = 0 + -25.66666667

Reorder the terms:
25.66666667 + -25.66666667 + -6.666666667x + x2 = 0 + -25.66666667

Combine like terms: 25.66666667 + -25.66666667 = 0.00000000
0.00000000 + -6.666666667x + x2 = 0 + -25.66666667
-6.666666667x + x2 = 0 + -25.66666667

Combine like terms: 0 + -25.66666667 = -25.66666667
-6.666666667x + x2 = -25.66666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -25.66666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -25.66666667 + 11.11111112

Combine like terms: -25.66666667 + 11.11111112 = -14.55555555
11.11111112 + -6.666666667x + x2 = -14.55555555

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = -14.55555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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