4x-2+3x=2-3x(2x+5)-3

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Solution for 4x-2+3x=2-3x(2x+5)-3 equation:


Simplifying
4x + -2 + 3x = 2 + -3x(2x + 5) + -3

Reorder the terms:
-2 + 4x + 3x = 2 + -3x(2x + 5) + -3

Combine like terms: 4x + 3x = 7x
-2 + 7x = 2 + -3x(2x + 5) + -3

Reorder the terms:
-2 + 7x = 2 + -3x(5 + 2x) + -3
-2 + 7x = 2 + (5 * -3x + 2x * -3x) + -3
-2 + 7x = 2 + (-15x + -6x2) + -3

Reorder the terms:
-2 + 7x = 2 + -3 + -15x + -6x2

Combine like terms: 2 + -3 = -1
-2 + 7x = -1 + -15x + -6x2

Solving
-2 + 7x = -1 + -15x + -6x2

Solving for variable 'x'.

Reorder the terms:
-2 + 1 + 7x + 15x + 6x2 = -1 + -15x + -6x2 + 1 + 15x + 6x2

Combine like terms: -2 + 1 = -1
-1 + 7x + 15x + 6x2 = -1 + -15x + -6x2 + 1 + 15x + 6x2

Combine like terms: 7x + 15x = 22x
-1 + 22x + 6x2 = -1 + -15x + -6x2 + 1 + 15x + 6x2

Reorder the terms:
-1 + 22x + 6x2 = -1 + 1 + -15x + 15x + -6x2 + 6x2

Combine like terms: -1 + 1 = 0
-1 + 22x + 6x2 = 0 + -15x + 15x + -6x2 + 6x2
-1 + 22x + 6x2 = -15x + 15x + -6x2 + 6x2

Combine like terms: -15x + 15x = 0
-1 + 22x + 6x2 = 0 + -6x2 + 6x2
-1 + 22x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-1 + 22x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 3.666666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 3.666666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 3.666666667x + x2 = 0 + 0.1666666667
3.666666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
3.666666667x + x2 = 0.1666666667

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 0.1666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 0.1666666667 + 3.361111114

Combine like terms: 0.1666666667 + 3.361111114 = 3.5277777807
3.361111114 + 3.666666667x + x2 = 3.5277777807

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 3.5277777807

Calculate the square root of the right side: 1.878237946

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 1.878237946 and -1.878237946.


Subproblem 1
x + 1.833333334 = 1.878237946

Simplifying
x + 1.833333334 = 1.878237946

Reorder the terms:
1.833333334 + x = 1.878237946

Solving
1.833333334 + x = 1.878237946

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 1.878237946 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 1.878237946 + -1.833333334
x = 1.878237946 + -1.833333334

Combine like terms: 1.878237946 + -1.833333334 = 0.044904612
x = 0.044904612

Simplifying
x = 0.044904612


Subproblem 2
x + 1.833333334 = -1.878237946

Simplifying
x + 1.833333334 = -1.878237946

Reorder the terms:
1.833333334 + x = -1.878237946

Solving
1.833333334 + x = -1.878237946

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -1.878237946 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -1.878237946 + -1.833333334
x = -1.878237946 + -1.833333334

Combine like terms: -1.878237946 + -1.833333334 = -3.71157128
x = -3.71157128

Simplifying
x = -3.71157128


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.044904612, -3.71157128}

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