(x-7)(3x+1)+84=(x-5)(2x-7)

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Solution for (x-7)(3x+1)+84=(x-5)(2x-7) equation: 


Simplifying
(x + -7)(3x + 1) + 84 = (x + -5)(2x + -7)

Reorder the terms:
(-7 + x)(3x + 1) + 84 = (x + -5)(2x + -7)

Reorder the terms:
(-7 + x)(1 + 3x) + 84 = (x + -5)(2x + -7)

Multiply (-7 + x) * (1 + 3x)
(-7(1 + 3x) + x(1 + 3x)) + 84 = (x + -5)(2x + -7)
((1 * -7 + 3x * -7) + x(1 + 3x)) + 84 = (x + -5)(2x + -7)
((-7 + -21x) + x(1 + 3x)) + 84 = (x + -5)(2x + -7)
(-7 + -21x + (1 * x + 3x * x)) + 84 = (x + -5)(2x + -7)
(-7 + -21x + (1x + 3x2)) + 84 = (x + -5)(2x + -7)

Combine like terms: -21x + 1x = -20x
(-7 + -20x + 3x2) + 84 = (x + -5)(2x + -7)

Reorder the terms:
-7 + 84 + -20x + 3x2 = (x + -5)(2x + -7)

Combine like terms: -7 + 84 = 77
77 + -20x + 3x2 = (x + -5)(2x + -7)

Reorder the terms:
77 + -20x + 3x2 = (-5 + x)(2x + -7)

Reorder the terms:
77 + -20x + 3x2 = (-5 + x)(-7 + 2x)

Multiply (-5 + x) * (-7 + 2x)
77 + -20x + 3x2 = (-5(-7 + 2x) + x(-7 + 2x))
77 + -20x + 3x2 = ((-7 * -5 + 2x * -5) + x(-7 + 2x))
77 + -20x + 3x2 = ((35 + -10x) + x(-7 + 2x))
77 + -20x + 3x2 = (35 + -10x + (-7 * x + 2x * x))
77 + -20x + 3x2 = (35 + -10x + (-7x + 2x2))

Combine like terms: -10x + -7x = -17x
77 + -20x + 3x2 = (35 + -17x + 2x2)

Solving
77 + -20x + 3x2 = 35 + -17x + 2x2

Solving for variable 'x'.

Reorder the terms:
77 + -35 + -20x + 17x + 3x2 + -2x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Combine like terms: 77 + -35 = 42
42 + -20x + 17x + 3x2 + -2x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Combine like terms: -20x + 17x = -3x
42 + -3x + 3x2 + -2x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
42 + -3x + 1x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Reorder the terms:
42 + -3x + 1x2 = 35 + -35 + -17x + 17x + 2x2 + -2x2

Combine like terms: 35 + -35 = 0
42 + -3x + 1x2 = 0 + -17x + 17x + 2x2 + -2x2
42 + -3x + 1x2 = -17x + 17x + 2x2 + -2x2

Combine like terms: -17x + 17x = 0
42 + -3x + 1x2 = 0 + 2x2 + -2x2
42 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + -3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -3x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -3x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -3x + x2 = 0 + -42
-3x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-3x + x2 = -42

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -42 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -42 + 2.25

Combine like terms: -42 + 2.25 = -39.75
2.25 + -3x + x2 = -39.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -39.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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