(5x+18)(-2x+12)=58

Solution for (5x+18)(-2x+12)=58 equation:

Simplifying
(5x + 18)(-2x + 12) = 58

Reorder the terms:
(18 + 5x)(-2x + 12) = 58

Reorder the terms:
(18 + 5x)(12 + -2x) = 58

Multiply (18 + 5x) * (12 + -2x)
(18(12 + -2x) + 5x * (12 + -2x)) = 58
((12 * 18 + -2x * 18) + 5x * (12 + -2x)) = 58
((216 + -36x) + 5x * (12 + -2x)) = 58
(216 + -36x + (12 * 5x + -2x * 5x)) = 58
(216 + -36x + (60x + -10x2)) = 58

Combine like terms: -36x + 60x = 24x
(216 + 24x + -10x2) = 58

Solving
216 + 24x + -10x2 = 58

Solving for variable 'x'.

Reorder the terms:
216 + -58 + 24x + -10x2 = 58 + -58

Combine like terms: 216 + -58 = 158
158 + 24x + -10x2 = 58 + -58

Combine like terms: 58 + -58 = 0
158 + 24x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(79 + 12x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(79 + 12x + -5x2)' equal to zero and attempt to solve:

Simplifying
79 + 12x + -5x2 = 0

Solving
79 + 12x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-15.8 + -2.4x + x2 = 0

Move the constant term to the right:

Add '15.8' to each side of the equation.
-15.8 + -2.4x + 15.8 + x2 = 0 + 15.8

Reorder the terms:
-15.8 + 15.8 + -2.4x + x2 = 0 + 15.8

Combine like terms: -15.8 + 15.8 = 0.0
0.0 + -2.4x + x2 = 0 + 15.8
-2.4x + x2 = 0 + 15.8

Combine like terms: 0 + 15.8 = 15.8
-2.4x + x2 = 15.8

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 15.8 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 15.8 + 1.44

Combine like terms: 15.8 + 1.44 = 17.24
1.44 + -2.4x + x2 = 17.24

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 17.24

Calculate the square root of the right side: 4.152107898

Break this problem into two subproblems by setting 
(x + -1.2) equal to 4.152107898 and -4.152107898.

Subproblem 1
x + -1.2 = 4.152107898

Simplifying
x + -1.2 = 4.152107898

Reorder the terms:
-1.2 + x = 4.152107898

Solving
-1.2 + x = 4.152107898

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 4.152107898 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 4.152107898 + 1.2
x = 4.152107898 + 1.2

Combine like terms: 4.152107898 + 1.2 = 5.352107898
x = 5.352107898

Simplifying
x = 5.352107898

Subproblem 2
x + -1.2 = -4.152107898

Simplifying
x + -1.2 = -4.152107898

Reorder the terms:
-1.2 + x = -4.152107898

Solving
-1.2 + x = -4.152107898

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -4.152107898 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -4.152107898 + 1.2
x = -4.152107898 + 1.2

Combine like terms: -4.152107898 + 1.2 = -2.952107898
x = -2.952107898

Simplifying
x = -2.952107898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.352107898, -2.952107898}
Solution
x = {5.352107898, -2.952107898}