10x(7x-5)=300

Solution for 10x(7x-5)=300 equation:

Simplifying
10x(7x + -5) = 300

Reorder the terms:
10x(-5 + 7x) = 300
(-5 * 10x + 7x * 10x) = 300
(-50x + 70x2) = 300

Solving
-50x + 70x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + -50x + 70x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + -50x + 70x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-30 + -5x + 7x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-30 + -5x + 7x2)' equal to zero and attempt to solve:

Simplifying
-30 + -5x + 7x2 = 0

Solving
-30 + -5x + 7x2 = 0

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

Divide each side by '7'.
-4.285714286 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '4.285714286' to each side of the equation.
-4.285714286 + -0.7142857143x + 4.285714286 + x2 = 0 + 4.285714286

Reorder the terms:
-4.285714286 + 4.285714286 + -0.7142857143x + x2 = 0 + 4.285714286

Combine like terms: -4.285714286 + 4.285714286 = 0.000000000
0.000000000 + -0.7142857143x + x2 = 0 + 4.285714286
-0.7142857143x + x2 = 0 + 4.285714286

Combine like terms: 0 + 4.285714286 = 4.285714286
-0.7142857143x + x2 = 4.285714286

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = 4.285714286 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = 4.285714286 + 0.1275510204

Combine like terms: 4.285714286 + 0.1275510204 = 4.4132653064
0.1275510204 + -0.7142857143x + x2 = 4.4132653064

Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = 4.4132653064

Calculate the square root of the right side: 2.10077731

Break this problem into two subproblems by setting 
(x + -0.3571428572) equal to 2.10077731 and -2.10077731.

Subproblem 1
x + -0.3571428572 = 2.10077731

Simplifying
x + -0.3571428572 = 2.10077731

Reorder the terms:
-0.3571428572 + x = 2.10077731

Solving
-0.3571428572 + x = 2.10077731

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = 2.10077731 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = 2.10077731 + 0.3571428572
x = 2.10077731 + 0.3571428572

Combine like terms: 2.10077731 + 0.3571428572 = 2.4579201672
x = 2.4579201672

Simplifying
x = 2.4579201672

Subproblem 2
x + -0.3571428572 = -2.10077731

Simplifying
x + -0.3571428572 = -2.10077731

Reorder the terms:
-0.3571428572 + x = -2.10077731

Solving
-0.3571428572 + x = -2.10077731

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = -2.10077731 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = -2.10077731 + 0.3571428572
x = -2.10077731 + 0.3571428572

Combine like terms: -2.10077731 + 0.3571428572 = -1.7436344528
x = -1.7436344528

Simplifying
x = -1.7436344528

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4579201672, -1.7436344528}
Solution
x = {2.4579201672, -1.7436344528}