(4x-28x+49)-6(12x-42)(x-3)=0

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Solution for (4x-28x+49)-6(12x-42)(x-3)=0 equation:


Simplifying
(4x + -28x + 49) + -6(12x + -42)(x + -3) = 0

Reorder the terms:
(49 + 4x + -28x) + -6(12x + -42)(x + -3) = 0

Combine like terms: 4x + -28x = -24x
(49 + -24x) + -6(12x + -42)(x + -3) = 0

Remove parenthesis around (49 + -24x)
49 + -24x + -6(12x + -42)(x + -3) = 0

Reorder the terms:
49 + -24x + -6(-42 + 12x)(x + -3) = 0

Reorder the terms:
49 + -24x + -6(-42 + 12x)(-3 + x) = 0

Multiply (-42 + 12x) * (-3 + x)
49 + -24x + -6(-42(-3 + x) + 12x * (-3 + x)) = 0
49 + -24x + -6((-3 * -42 + x * -42) + 12x * (-3 + x)) = 0
49 + -24x + -6((126 + -42x) + 12x * (-3 + x)) = 0
49 + -24x + -6(126 + -42x + (-3 * 12x + x * 12x)) = 0
49 + -24x + -6(126 + -42x + (-36x + 12x2)) = 0

Combine like terms: -42x + -36x = -78x
49 + -24x + -6(126 + -78x + 12x2) = 0
49 + -24x + (126 * -6 + -78x * -6 + 12x2 * -6) = 0
49 + -24x + (-756 + 468x + -72x2) = 0

Reorder the terms:
49 + -756 + -24x + 468x + -72x2 = 0

Combine like terms: 49 + -756 = -707
-707 + -24x + 468x + -72x2 = 0

Combine like terms: -24x + 468x = 444x
-707 + 444x + -72x2 = 0

Solving
-707 + 444x + -72x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-72 the coefficient of the squared term: 

Divide each side by '-72'.
9.819444444 + -6.166666667x + x2 = 0

Move the constant term to the right:

Add '-9.819444444' to each side of the equation.
9.819444444 + -6.166666667x + -9.819444444 + x2 = 0 + -9.819444444

Reorder the terms:
9.819444444 + -9.819444444 + -6.166666667x + x2 = 0 + -9.819444444

Combine like terms: 9.819444444 + -9.819444444 = 0.000000000
0.000000000 + -6.166666667x + x2 = 0 + -9.819444444
-6.166666667x + x2 = 0 + -9.819444444

Combine like terms: 0 + -9.819444444 = -9.819444444
-6.166666667x + x2 = -9.819444444

The x term is -6.166666667x.  Take half its coefficient (-3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
-6.166666667x + 9.506944449 + x2 = -9.819444444 + 9.506944449

Reorder the terms:
9.506944449 + -6.166666667x + x2 = -9.819444444 + 9.506944449

Combine like terms: -9.819444444 + 9.506944449 = -0.312499995
9.506944449 + -6.166666667x + x2 = -0.312499995

Factor a perfect square on the left side:
(x + -3.083333334)(x + -3.083333334) = -0.312499995

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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