(3x-7)(5x+5)=10

Solution for (3x-7)(5x+5)=10 equation:

Simplifying
(3x + -7)(5x + 5) = 10

Reorder the terms:
(-7 + 3x)(5x + 5) = 10

Reorder the terms:
(-7 + 3x)(5 + 5x) = 10

Multiply (-7 + 3x) * (5 + 5x)
(-7(5 + 5x) + 3x * (5 + 5x)) = 10
((5 * -7 + 5x * -7) + 3x * (5 + 5x)) = 10
((-35 + -35x) + 3x * (5 + 5x)) = 10
(-35 + -35x + (5 * 3x + 5x * 3x)) = 10
(-35 + -35x + (15x + 15x2)) = 10

Combine like terms: -35x + 15x = -20x
(-35 + -20x + 15x2) = 10

Solving
-35 + -20x + 15x2 = 10

Solving for variable 'x'.

Reorder the terms:
-35 + -10 + -20x + 15x2 = 10 + -10

Combine like terms: -35 + -10 = -45
-45 + -20x + 15x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-45 + -20x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + -4x + 3x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-9 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-9 + -4x + 3x2 = 0

Solving
-9 + -4x + 3x2 = 0

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

Divide each side by '3'.
-3 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.333333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.333333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.333333333x + x2 = 0 + 3
-1.333333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.333333333x + x2 = 3

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 3 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 3 + 0.4444444442

Combine like terms: 3 + 0.4444444442 = 3.4444444442
0.4444444442 + -1.333333333x + x2 = 3.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 3.4444444442

Calculate the square root of the right side: 1.855921454

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.855921454 and -1.855921454.

Subproblem 1
x + -0.6666666665 = 1.855921454

Simplifying
x + -0.6666666665 = 1.855921454

Reorder the terms:
-0.6666666665 + x = 1.855921454

Solving
-0.6666666665 + x = 1.855921454

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 1.855921454 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 1.855921454 + 0.6666666665
x = 1.855921454 + 0.6666666665

Combine like terms: 1.855921454 + 0.6666666665 = 2.5225881205
x = 2.5225881205

Simplifying
x = 2.5225881205

Subproblem 2
x + -0.6666666665 = -1.855921454

Simplifying
x + -0.6666666665 = -1.855921454

Reorder the terms:
-0.6666666665 + x = -1.855921454

Solving
-0.6666666665 + x = -1.855921454

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -1.855921454 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -1.855921454 + 0.6666666665
x = -1.855921454 + 0.6666666665

Combine like terms: -1.855921454 + 0.6666666665 = -1.1892547875
x = -1.1892547875

Simplifying
x = -1.1892547875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5225881205, -1.1892547875}
Solution
x = {2.5225881205, -1.1892547875}