(5x-2)(2x+3)=10

Solution for (5x-2)(2x+3)=10 equation:

Simplifying
(5x + -2)(2x + 3) = 10

Reorder the terms:
(-2 + 5x)(2x + 3) = 10

Reorder the terms:
(-2 + 5x)(3 + 2x) = 10

Multiply (-2 + 5x) * (3 + 2x)
(-2(3 + 2x) + 5x * (3 + 2x)) = 10
((3 * -2 + 2x * -2) + 5x * (3 + 2x)) = 10
((-6 + -4x) + 5x * (3 + 2x)) = 10
(-6 + -4x + (3 * 5x + 2x * 5x)) = 10
(-6 + -4x + (15x + 10x2)) = 10

Combine like terms: -4x + 15x = 11x
(-6 + 11x + 10x2) = 10

Solving
-6 + 11x + 10x2 = 10

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + 11x + 10x2 = 10 + -10

Combine like terms: -6 + -10 = -16
-16 + 11x + 10x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-16 + 11x + 10x2 = 0

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

Divide each side by '10'.
-1.6 + 1.1x + x2 = 0.0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 1.1x + 1.6 + x2 = 0.0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 1.1x + x2 = 0.0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 1.1x + x2 = 0.0 + 1.6
1.1x + x2 = 0.0 + 1.6

Combine like terms: 0.0 + 1.6 = 1.6
1.1x + x2 = 1.6

The x term is 1.1x.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1x + 0.3025 + x2 = 1.6 + 0.3025

Reorder the terms:
0.3025 + 1.1x + x2 = 1.6 + 0.3025

Combine like terms: 1.6 + 0.3025 = 1.9025
0.3025 + 1.1x + x2 = 1.9025

Factor a perfect square on the left side:
(x + 0.55)(x + 0.55) = 1.9025

Calculate the square root of the right side: 1.379311422

Break this problem into two subproblems by setting 
(x + 0.55) equal to 1.379311422 and -1.379311422.

Subproblem 1
x + 0.55 = 1.379311422

Simplifying
x + 0.55 = 1.379311422

Reorder the terms:
0.55 + x = 1.379311422

Solving
0.55 + x = 1.379311422

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = 1.379311422 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = 1.379311422 + -0.55
x = 1.379311422 + -0.55

Combine like terms: 1.379311422 + -0.55 = 0.829311422
x = 0.829311422

Simplifying
x = 0.829311422

Subproblem 2
x + 0.55 = -1.379311422

Simplifying
x + 0.55 = -1.379311422

Reorder the terms:
0.55 + x = -1.379311422

Solving
0.55 + x = -1.379311422

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = -1.379311422 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = -1.379311422 + -0.55
x = -1.379311422 + -0.55

Combine like terms: -1.379311422 + -0.55 = -1.929311422
x = -1.929311422

Simplifying
x = -1.929311422

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.829311422, -1.929311422}