7x+5(x+3)4x-x-2=

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Solution for 7x+5(x+3)4x-x-2= equation: 


Simplifying
7x + 5(x + 3) * 4x + -1x + -2 = 0

Reorder the terms:
7x + 5(3 + x) * 4x + -1x + -2 = 0

Reorder the terms for easier multiplication:
7x + 5 * 4x(3 + x) + -1x + -2 = 0

Multiply 5 * 4
7x + 20x(3 + x) + -1x + -2 = 0
7x + (3 * 20x + x * 20x) + -1x + -2 = 0
7x + (60x + 20x2) + -1x + -2 = 0

Reorder the terms:
-2 + 7x + 60x + -1x + 20x2 = 0

Combine like terms: 7x + 60x = 67x
-2 + 67x + -1x + 20x2 = 0

Combine like terms: 67x + -1x = 66x
-2 + 66x + 20x2 = 0

Solving
-2 + 66x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 33x + 10x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 33x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + 33x + 10x2 = 0

Solving
-1 + 33x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + 3.3x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 3.3x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 3.3x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 3.3x + x2 = 0.0 + 0.1
3.3x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
3.3x + x2 = 0.1

The x term is 3.3x.  Take half its coefficient (1.65).
Square it (2.7225) and add it to both sides.

Add '2.7225' to each side of the equation.
3.3x + 2.7225 + x2 = 0.1 + 2.7225

Reorder the terms:
2.7225 + 3.3x + x2 = 0.1 + 2.7225

Combine like terms: 0.1 + 2.7225 = 2.8225
2.7225 + 3.3x + x2 = 2.8225

Factor a perfect square on the left side:
(x + 1.65)(x + 1.65) = 2.8225

Calculate the square root of the right side: 1.680029762

Break this problem into two subproblems by setting 
(x + 1.65) equal to 1.680029762 and -1.680029762.


Subproblem 1
x + 1.65 = 1.680029762

Simplifying
x + 1.65 = 1.680029762

Reorder the terms:
1.65 + x = 1.680029762

Solving
1.65 + x = 1.680029762

Solving for variable 'x'.

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

Add '-1.65' to each side of the equation.
1.65 + -1.65 + x = 1.680029762 + -1.65

Combine like terms: 1.65 + -1.65 = 0.00
0.00 + x = 1.680029762 + -1.65
x = 1.680029762 + -1.65

Combine like terms: 1.680029762 + -1.65 = 0.030029762
x = 0.030029762

Simplifying
x = 0.030029762


Subproblem 2
x + 1.65 = -1.680029762

Simplifying
x + 1.65 = -1.680029762

Reorder the terms:
1.65 + x = -1.680029762

Solving
1.65 + x = -1.680029762

Solving for variable 'x'.

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

Add '-1.65' to each side of the equation.
1.65 + -1.65 + x = -1.680029762 + -1.65

Combine like terms: 1.65 + -1.65 = 0.00
0.00 + x = -1.680029762 + -1.65
x = -1.680029762 + -1.65

Combine like terms: -1.680029762 + -1.65 = -3.330029762
x = -3.330029762

Simplifying
x = -3.330029762


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.030029762, -3.330029762}
Solution
x = {0.030029762, -3.330029762}

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