-3x(x-7)+2x(3-x)=21

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Solution for -3x(x-7)+2x(3-x)=21 equation: 


Simplifying
-3x(x + -7) + 2x(3 + -1x) = 21

Reorder the terms:
-3x(-7 + x) + 2x(3 + -1x) = 21
(-7 * -3x + x * -3x) + 2x(3 + -1x) = 21
(21x + -3x2) + 2x(3 + -1x) = 21
21x + -3x2 + (3 * 2x + -1x * 2x) = 21
21x + -3x2 + (6x + -2x2) = 21

Reorder the terms:
21x + 6x + -3x2 + -2x2 = 21

Combine like terms: 21x + 6x = 27x
27x + -3x2 + -2x2 = 21

Combine like terms: -3x2 + -2x2 = -5x2
27x + -5x2 = 21

Solving
27x + -5x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 27x + -5x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 27x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
4.2 + -5.4x + x2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + -5.4x + -4.2 + x2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + -5.4x + x2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + -5.4x + x2 = 0 + -4.2
-5.4x + x2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
-5.4x + x2 = -4.2

The x term is -5.4x.  Take half its coefficient (-2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
-5.4x + 7.29 + x2 = -4.2 + 7.29

Reorder the terms:
7.29 + -5.4x + x2 = -4.2 + 7.29

Combine like terms: -4.2 + 7.29 = 3.09
7.29 + -5.4x + x2 = 3.09

Factor a perfect square on the left side:
(x + -2.7)(x + -2.7) = 3.09

Calculate the square root of the right side: 1.757839583

Break this problem into two subproblems by setting 
(x + -2.7) equal to 1.757839583 and -1.757839583.


Subproblem 1
x + -2.7 = 1.757839583

Simplifying
x + -2.7 = 1.757839583

Reorder the terms:
-2.7 + x = 1.757839583

Solving
-2.7 + x = 1.757839583

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = 1.757839583 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = 1.757839583 + 2.7
x = 1.757839583 + 2.7

Combine like terms: 1.757839583 + 2.7 = 4.457839583
x = 4.457839583

Simplifying
x = 4.457839583


Subproblem 2
x + -2.7 = -1.757839583

Simplifying
x + -2.7 = -1.757839583

Reorder the terms:
-2.7 + x = -1.757839583

Solving
-2.7 + x = -1.757839583

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = -1.757839583 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = -1.757839583 + 2.7
x = -1.757839583 + 2.7

Combine like terms: -1.757839583 + 2.7 = 0.942160417
x = 0.942160417

Simplifying
x = 0.942160417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.457839583, 0.942160417}

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