56+x(-3x+5)=-21x

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Solution for 56+x(-3x+5)=-21x equation: 


Simplifying
56 + x(-3x + 5) = -21x

Reorder the terms:
56 + x(5 + -3x) = -21x
56 + (5 * x + -3x * x) = -21x
56 + (5x + -3x2) = -21x

Solving
56 + 5x + -3x2 = -21x

Solving for variable 'x'.

Reorder the terms:
56 + 5x + 21x + -3x2 = -21x + 21x

Combine like terms: 5x + 21x = 26x
56 + 26x + -3x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
56 + 26x + -3x2 = 0

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

Divide each side by '-3'.
-18.66666667 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -8.666666667x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -8.666666667x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -8.666666667x + x2 = 0 + 18.66666667
-8.666666667x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-8.666666667x + x2 = 18.66666667

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 18.66666667 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 18.66666667 + 18.77777778

Combine like terms: 18.66666667 + 18.77777778 = 37.44444445
18.77777778 + -8.666666667x + x2 = 37.44444445

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 37.44444445

Calculate the square root of the right side: 6.119186584

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 6.119186584 and -6.119186584.


Subproblem 1
x + -4.333333334 = 6.119186584

Simplifying
x + -4.333333334 = 6.119186584

Reorder the terms:
-4.333333334 + x = 6.119186584

Solving
-4.333333334 + x = 6.119186584

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 6.119186584 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 6.119186584 + 4.333333334
x = 6.119186584 + 4.333333334

Combine like terms: 6.119186584 + 4.333333334 = 10.452519918
x = 10.452519918

Simplifying
x = 10.452519918


Subproblem 2
x + -4.333333334 = -6.119186584

Simplifying
x + -4.333333334 = -6.119186584

Reorder the terms:
-4.333333334 + x = -6.119186584

Solving
-4.333333334 + x = -6.119186584

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -6.119186584 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -6.119186584 + 4.333333334
x = -6.119186584 + 4.333333334

Combine like terms: -6.119186584 + 4.333333334 = -1.78585325
x = -1.78585325

Simplifying
x = -1.78585325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.452519918, -1.78585325}

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