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

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

Simplifying
5x + -3 = 3(x + 7) * 3x

Reorder the terms:
-3 + 5x = 3(x + 7) * 3x

Reorder the terms:
-3 + 5x = 3(7 + x) * 3x

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

Multiply 3 * 3
-3 + 5x = 9x(7 + x)
-3 + 5x = (7 * 9x + x * 9x)
-3 + 5x = (63x + 9x2)

Solving
-3 + 5x = 63x + 9x2

Solving for variable 'x'.

Combine like terms: 5x + -63x = -58x
-3 + -58x + -9x2 = 63x + 9x2 + -63x + -9x2

Reorder the terms:
-3 + -58x + -9x2 = 63x + -63x + 9x2 + -9x2

Combine like terms: 63x + -63x = 0
-3 + -58x + -9x2 = 0 + 9x2 + -9x2
-3 + -58x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-3 + -58x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 58x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 58x + 9x2)' equal to zero and attempt to solve:

Simplifying
3 + 58x + 9x2 = 0

Solving
3 + 58x + 9x2 = 0

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

Divide each side by '9'.
0.3333333333 + 6.444444444x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 6.444444444x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 6.444444444x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 6.444444444x + x2 = 0 + -0.3333333333
6.444444444x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
6.444444444x + x2 = -0.3333333333

The x term is 6.444444444x.  Take half its coefficient (3.222222222).
Square it (10.38271605) and add it to both sides.

Add '10.38271605' to each side of the equation.
6.444444444x + 10.38271605 + x2 = -0.3333333333 + 10.38271605

Reorder the terms:
10.38271605 + 6.444444444x + x2 = -0.3333333333 + 10.38271605

Combine like terms: -0.3333333333 + 10.38271605 = 10.0493827167
10.38271605 + 6.444444444x + x2 = 10.0493827167

Factor a perfect square on the left side:
(x + 3.222222222)(x + 3.222222222) = 10.0493827167

Calculate the square root of the right side: 3.170076137

Break this problem into two subproblems by setting 
(x + 3.222222222) equal to 3.170076137 and -3.170076137.

Subproblem 1
x + 3.222222222 = 3.170076137

Simplifying
x + 3.222222222 = 3.170076137

Reorder the terms:
3.222222222 + x = 3.170076137

Solving
3.222222222 + x = 3.170076137

Solving for variable 'x'.

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

Add '-3.222222222' to each side of the equation.
3.222222222 + -3.222222222 + x = 3.170076137 + -3.222222222

Combine like terms: 3.222222222 + -3.222222222 = 0.000000000
0.000000000 + x = 3.170076137 + -3.222222222
x = 3.170076137 + -3.222222222

Combine like terms: 3.170076137 + -3.222222222 = -0.052146085
x = -0.052146085

Simplifying
x = -0.052146085

Subproblem 2
x + 3.222222222 = -3.170076137

Simplifying
x + 3.222222222 = -3.170076137

Reorder the terms:
3.222222222 + x = -3.170076137

Solving
3.222222222 + x = -3.170076137

Solving for variable 'x'.

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

Add '-3.222222222' to each side of the equation.
3.222222222 + -3.222222222 + x = -3.170076137 + -3.222222222

Combine like terms: 3.222222222 + -3.222222222 = 0.000000000
0.000000000 + x = -3.170076137 + -3.222222222
x = -3.170076137 + -3.222222222

Combine like terms: -3.170076137 + -3.222222222 = -6.392298359
x = -6.392298359

Simplifying
x = -6.392298359

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.052146085, -6.392298359}
Solution
x = {-0.052146085, -6.392298359}