(2x-5)*(3x+2)-(x^2-5x)*3=

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Solution for (2x-5)*(3x+2)-(x^2-5x)*3= equation: 


Simplifying
(2x + -5)(3x + 2) + -1(x2 + -5x) * 3 = 0

Reorder the terms:
(-5 + 2x)(3x + 2) + -1(x2 + -5x) * 3 = 0

Reorder the terms:
(-5 + 2x)(2 + 3x) + -1(x2 + -5x) * 3 = 0

Multiply (-5 + 2x) * (2 + 3x)
(-5(2 + 3x) + 2x * (2 + 3x)) + -1(x2 + -5x) * 3 = 0
((2 * -5 + 3x * -5) + 2x * (2 + 3x)) + -1(x2 + -5x) * 3 = 0
((-10 + -15x) + 2x * (2 + 3x)) + -1(x2 + -5x) * 3 = 0
(-10 + -15x + (2 * 2x + 3x * 2x)) + -1(x2 + -5x) * 3 = 0
(-10 + -15x + (4x + 6x2)) + -1(x2 + -5x) * 3 = 0

Combine like terms: -15x + 4x = -11x
(-10 + -11x + 6x2) + -1(x2 + -5x) * 3 = 0

Reorder the terms:
-10 + -11x + 6x2 + -1(-5x + x2) * 3 = 0

Reorder the terms for easier multiplication:
-10 + -11x + 6x2 + -1 * 3(-5x + x2) = 0

Multiply -1 * 3
-10 + -11x + 6x2 + -3(-5x + x2) = 0
-10 + -11x + 6x2 + (-5x * -3 + x2 * -3) = 0
-10 + -11x + 6x2 + (15x + -3x2) = 0

Reorder the terms:
-10 + -11x + 15x + 6x2 + -3x2 = 0

Combine like terms: -11x + 15x = 4x
-10 + 4x + 6x2 + -3x2 = 0

Combine like terms: 6x2 + -3x2 = 3x2
-10 + 4x + 3x2 = 0

Solving
-10 + 4x + 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'.
-3.333333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 1.333333333x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 1.333333333x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 3.333333333
1.333333333x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
1.333333333x + x2 = 3.333333333

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 3.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 3.333333333 + 0.4444444442

Combine like terms: 3.333333333 + 0.4444444442 = 3.7777777772
0.4444444442 + 1.333333333x + x2 = 3.7777777772

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 3.7777777772

Calculate the square root of the right side: 1.943650631

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.943650631 and -1.943650631.


Subproblem 1
x + 0.6666666665 = 1.943650631

Simplifying
x + 0.6666666665 = 1.943650631

Reorder the terms:
0.6666666665 + x = 1.943650631

Solving
0.6666666665 + x = 1.943650631

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.943650631 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.943650631 + -0.6666666665
x = 1.943650631 + -0.6666666665

Combine like terms: 1.943650631 + -0.6666666665 = 1.2769839645
x = 1.2769839645

Simplifying
x = 1.2769839645


Subproblem 2
x + 0.6666666665 = -1.943650631

Simplifying
x + 0.6666666665 = -1.943650631

Reorder the terms:
0.6666666665 + x = -1.943650631

Solving
0.6666666665 + x = -1.943650631

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.943650631 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.943650631 + -0.6666666665
x = -1.943650631 + -0.6666666665

Combine like terms: -1.943650631 + -0.6666666665 = -2.6103172975
x = -2.6103172975

Simplifying
x = -2.6103172975


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2769839645, -2.6103172975}

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