42x(5+8x)=(5x+6)(9-3x)

Solution for 42x(5+8x)=(5x+6)(9-3x) equation:

Simplifying
42x(5 + 8x) = (5x + 6)(9 + -3x)
(5 * 42x + 8x * 42x) = (5x + 6)(9 + -3x)
(210x + 336x2) = (5x + 6)(9 + -3x)

Reorder the terms:
210x + 336x2 = (6 + 5x)(9 + -3x)

Multiply (6 + 5x) * (9 + -3x)
210x + 336x2 = (6(9 + -3x) + 5x * (9 + -3x))
210x + 336x2 = ((9 * 6 + -3x * 6) + 5x * (9 + -3x))
210x + 336x2 = ((54 + -18x) + 5x * (9 + -3x))
210x + 336x2 = (54 + -18x + (9 * 5x + -3x * 5x))
210x + 336x2 = (54 + -18x + (45x + -15x2))

Combine like terms: -18x + 45x = 27x
210x + 336x2 = (54 + 27x + -15x2)

Solving
210x + 336x2 = 54 + 27x + -15x2

Solving for variable 'x'.

Reorder the terms:
-54 + 210x + -27x + 336x2 + 15x2 = 54 + 27x + -15x2 + -54 + -27x + 15x2

Combine like terms: 210x + -27x = 183x
-54 + 183x + 336x2 + 15x2 = 54 + 27x + -15x2 + -54 + -27x + 15x2

Combine like terms: 336x2 + 15x2 = 351x2
-54 + 183x + 351x2 = 54 + 27x + -15x2 + -54 + -27x + 15x2

Reorder the terms:
-54 + 183x + 351x2 = 54 + -54 + 27x + -27x + -15x2 + 15x2

Combine like terms: 54 + -54 = 0
-54 + 183x + 351x2 = 0 + 27x + -27x + -15x2 + 15x2
-54 + 183x + 351x2 = 27x + -27x + -15x2 + 15x2

Combine like terms: 27x + -27x = 0
-54 + 183x + 351x2 = 0 + -15x2 + 15x2
-54 + 183x + 351x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
-54 + 183x + 351x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 61x + 117x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-18 + 61x + 117x2)' equal to zero and attempt to solve:

Simplifying
-18 + 61x + 117x2 = 0

Solving
-18 + 61x + 117x2 = 0

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

Divide each side by '117'.
-0.1538461538 + 0.5213675214x + x2 = 0

Move the constant term to the right:

Add '0.1538461538' to each side of the equation.
-0.1538461538 + 0.5213675214x + 0.1538461538 + x2 = 0 + 0.1538461538

Reorder the terms:
-0.1538461538 + 0.1538461538 + 0.5213675214x + x2 = 0 + 0.1538461538

Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000
0.0000000000 + 0.5213675214x + x2 = 0 + 0.1538461538
0.5213675214x + x2 = 0 + 0.1538461538

Combine like terms: 0 + 0.1538461538 = 0.1538461538
0.5213675214x + x2 = 0.1538461538

The x term is 0.5213675214x.  Take half its coefficient (0.2606837607).
Square it (0.06795602309) and add it to both sides.

Add '0.06795602309' to each side of the equation.
0.5213675214x + 0.06795602309 + x2 = 0.1538461538 + 0.06795602309

Reorder the terms:
0.06795602309 + 0.5213675214x + x2 = 0.1538461538 + 0.06795602309

Combine like terms: 0.1538461538 + 0.06795602309 = 0.22180217689
0.06795602309 + 0.5213675214x + x2 = 0.22180217689

Factor a perfect square on the left side:
(x + 0.2606837607)(x + 0.2606837607) = 0.22180217689

Calculate the square root of the right side: 0.470958785

Break this problem into two subproblems by setting 
(x + 0.2606837607) equal to 0.470958785 and -0.470958785.

Subproblem 1
x + 0.2606837607 = 0.470958785

Simplifying
x + 0.2606837607 = 0.470958785

Reorder the terms:
0.2606837607 + x = 0.470958785

Solving
0.2606837607 + x = 0.470958785

Solving for variable 'x'.

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

Add '-0.2606837607' to each side of the equation.
0.2606837607 + -0.2606837607 + x = 0.470958785 + -0.2606837607

Combine like terms: 0.2606837607 + -0.2606837607 = 0.0000000000
0.0000000000 + x = 0.470958785 + -0.2606837607
x = 0.470958785 + -0.2606837607

Combine like terms: 0.470958785 + -0.2606837607 = 0.2102750243
x = 0.2102750243

Simplifying
x = 0.2102750243

Subproblem 2
x + 0.2606837607 = -0.470958785

Simplifying
x + 0.2606837607 = -0.470958785

Reorder the terms:
0.2606837607 + x = -0.470958785

Solving
0.2606837607 + x = -0.470958785

Solving for variable 'x'.

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

Add '-0.2606837607' to each side of the equation.
0.2606837607 + -0.2606837607 + x = -0.470958785 + -0.2606837607

Combine like terms: 0.2606837607 + -0.2606837607 = 0.0000000000
0.0000000000 + x = -0.470958785 + -0.2606837607
x = -0.470958785 + -0.2606837607

Combine like terms: -0.470958785 + -0.2606837607 = -0.7316425457
x = -0.7316425457

Simplifying
x = -0.7316425457

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2102750243, -0.7316425457}
Solution
x = {0.2102750243, -0.7316425457}