3x(4x+3-5)=58

Solution for 3x(4x+3-5)=58 equation:

Simplifying
3x(4x + 3 + -5) = 58

Reorder the terms:
3x(3 + -5 + 4x) = 58

Combine like terms: 3 + -5 = -2
3x(-2 + 4x) = 58
(-2 * 3x + 4x * 3x) = 58
(-6x + 12x2) = 58

Solving
-6x + 12x2 = 58

Solving for variable 'x'.

Reorder the terms:
-58 + -6x + 12x2 = 58 + -58

Combine like terms: 58 + -58 = 0
-58 + -6x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + -3x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-29 + -3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-29 + -3x + 6x2 = 0

Solving
-29 + -3x + 6x2 = 0

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

Divide each side by '6'.
-4.833333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '4.833333333' to each side of the equation.
-4.833333333 + -0.5x + 4.833333333 + x2 = 0 + 4.833333333

Reorder the terms:
-4.833333333 + 4.833333333 + -0.5x + x2 = 0 + 4.833333333

Combine like terms: -4.833333333 + 4.833333333 = 0.000000000
0.000000000 + -0.5x + x2 = 0 + 4.833333333
-0.5x + x2 = 0 + 4.833333333

Combine like terms: 0 + 4.833333333 = 4.833333333
-0.5x + x2 = 4.833333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 4.833333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 4.833333333 + 0.0625

Combine like terms: 4.833333333 + 0.0625 = 4.895833333
0.0625 + -0.5x + x2 = 4.895833333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 4.895833333

Calculate the square root of the right side: 2.212653008

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.212653008 and -2.212653008.

Subproblem 1
x + -0.25 = 2.212653008

Simplifying
x + -0.25 = 2.212653008

Reorder the terms:
-0.25 + x = 2.212653008

Solving
-0.25 + x = 2.212653008

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 2.212653008 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.212653008 + 0.25
x = 2.212653008 + 0.25

Combine like terms: 2.212653008 + 0.25 = 2.462653008
x = 2.462653008

Simplifying
x = 2.462653008

Subproblem 2
x + -0.25 = -2.212653008

Simplifying
x + -0.25 = -2.212653008

Reorder the terms:
-0.25 + x = -2.212653008

Solving
-0.25 + x = -2.212653008

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -2.212653008 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.212653008 + 0.25
x = -2.212653008 + 0.25

Combine like terms: -2.212653008 + 0.25 = -1.962653008
x = -1.962653008

Simplifying
x = -1.962653008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.462653008, -1.962653008}
Solution
x = {2.462653008, -1.962653008}