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

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


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

Reorder the terms:
-3x(2 + x) + -1(2x + -5) = 0
(2 * -3x + x * -3x) + -1(2x + -5) = 0
(-6x + -3x2) + -1(2x + -5) = 0

Reorder the terms:
-6x + -3x2 + -1(-5 + 2x) = 0
-6x + -3x2 + (-5 * -1 + 2x * -1) = 0
-6x + -3x2 + (5 + -2x) = 0

Reorder the terms:
5 + -6x + -2x + -3x2 = 0

Combine like terms: -6x + -2x = -8x
5 + -8x + -3x2 = 0

Solving
5 + -8x + -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'.
-1.666666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2.666666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2.666666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 1.666666667
2.666666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2.666666667x + x2 = 1.666666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 1.666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 1.666666667 + 1.777777780

Combine like terms: 1.666666667 + 1.777777780 = 3.444444447
1.777777780 + 2.666666667x + x2 = 3.444444447

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 3.444444447

Calculate the square root of the right side: 1.855921455

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.855921455 and -1.855921455.


Subproblem 1
x + 1.333333334 = 1.855921455

Simplifying
x + 1.333333334 = 1.855921455

Reorder the terms:
1.333333334 + x = 1.855921455

Solving
1.333333334 + x = 1.855921455

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 1.855921455 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 1.855921455 + -1.333333334
x = 1.855921455 + -1.333333334

Combine like terms: 1.855921455 + -1.333333334 = 0.522588121
x = 0.522588121

Simplifying
x = 0.522588121


Subproblem 2
x + 1.333333334 = -1.855921455

Simplifying
x + 1.333333334 = -1.855921455

Reorder the terms:
1.333333334 + x = -1.855921455

Solving
1.333333334 + x = -1.855921455

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -1.855921455 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -1.855921455 + -1.333333334
x = -1.855921455 + -1.333333334

Combine like terms: -1.855921455 + -1.333333334 = -3.189254789
x = -3.189254789

Simplifying
x = -3.189254789


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.522588121, -3.189254789}

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