4(5x+2)-3(x-2)=10x(7x+9)

Solution for 4(5x+2)-3(x-2)=10x(7x+9) equation:

Simplifying
4(5x + 2) + -3(x + -2) = 10x(7x + 9)

Reorder the terms:
4(2 + 5x) + -3(x + -2) = 10x(7x + 9)
(2 * 4 + 5x * 4) + -3(x + -2) = 10x(7x + 9)
(8 + 20x) + -3(x + -2) = 10x(7x + 9)

Reorder the terms:
8 + 20x + -3(-2 + x) = 10x(7x + 9)
8 + 20x + (-2 * -3 + x * -3) = 10x(7x + 9)
8 + 20x + (6 + -3x) = 10x(7x + 9)

Reorder the terms:
8 + 6 + 20x + -3x = 10x(7x + 9)

Combine like terms: 8 + 6 = 14
14 + 20x + -3x = 10x(7x + 9)

Combine like terms: 20x + -3x = 17x
14 + 17x = 10x(7x + 9)

Reorder the terms:
14 + 17x = 10x(9 + 7x)
14 + 17x = (9 * 10x + 7x * 10x)
14 + 17x = (90x + 70x2)

Solving
14 + 17x = 90x + 70x2

Solving for variable 'x'.

Combine like terms: 17x + -90x = -73x
14 + -73x + -70x2 = 90x + 70x2 + -90x + -70x2

Reorder the terms:
14 + -73x + -70x2 = 90x + -90x + 70x2 + -70x2

Combine like terms: 90x + -90x = 0
14 + -73x + -70x2 = 0 + 70x2 + -70x2
14 + -73x + -70x2 = 70x2 + -70x2

Combine like terms: 70x2 + -70x2 = 0
14 + -73x + -70x2 = 0

Begin completing the square.  Divide all terms by
-70 the coefficient of the squared term: 

Divide each side by '-70'.
-0.2 + 1.042857143x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1.042857143x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1.042857143x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1.042857143x + x2 = 0 + 0.2
1.042857143x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
1.042857143x + x2 = 0.2

The x term is 1.042857143x.  Take half its coefficient (0.5214285715).
Square it (0.2718877552) and add it to both sides.

Add '0.2718877552' to each side of the equation.
1.042857143x + 0.2718877552 + x2 = 0.2 + 0.2718877552

Reorder the terms:
0.2718877552 + 1.042857143x + x2 = 0.2 + 0.2718877552

Combine like terms: 0.2 + 0.2718877552 = 0.4718877552
0.2718877552 + 1.042857143x + x2 = 0.4718877552

Factor a perfect square on the left side:
(x + 0.5214285715)(x + 0.5214285715) = 0.4718877552

Calculate the square root of the right side: 0.686940867

Break this problem into two subproblems by setting 
(x + 0.5214285715) equal to 0.686940867 and -0.686940867.

Subproblem 1
x + 0.5214285715 = 0.686940867

Simplifying
x + 0.5214285715 = 0.686940867

Reorder the terms:
0.5214285715 + x = 0.686940867

Solving
0.5214285715 + x = 0.686940867

Solving for variable 'x'.

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

Add '-0.5214285715' to each side of the equation.
0.5214285715 + -0.5214285715 + x = 0.686940867 + -0.5214285715

Combine like terms: 0.5214285715 + -0.5214285715 = 0.0000000000
0.0000000000 + x = 0.686940867 + -0.5214285715
x = 0.686940867 + -0.5214285715

Combine like terms: 0.686940867 + -0.5214285715 = 0.1655122955
x = 0.1655122955

Simplifying
x = 0.1655122955

Subproblem 2
x + 0.5214285715 = -0.686940867

Simplifying
x + 0.5214285715 = -0.686940867

Reorder the terms:
0.5214285715 + x = -0.686940867

Solving
0.5214285715 + x = -0.686940867

Solving for variable 'x'.

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

Add '-0.5214285715' to each side of the equation.
0.5214285715 + -0.5214285715 + x = -0.686940867 + -0.5214285715

Combine like terms: 0.5214285715 + -0.5214285715 = 0.0000000000
0.0000000000 + x = -0.686940867 + -0.5214285715
x = -0.686940867 + -0.5214285715

Combine like terms: -0.686940867 + -0.5214285715 = -1.2083694385
x = -1.2083694385

Simplifying
x = -1.2083694385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1655122955, -1.2083694385}