(3x+10)(14x)=360

Solution for (3x+10)(14x)=360 equation:

Simplifying
(3x + 10)(14x) = 360

Reorder the terms:
(10 + 3x)(14x) = 360

Remove parenthesis around (14x)
(10 + 3x) * 14x = 360

Reorder the terms for easier multiplication:
14x(10 + 3x) = 360
(10 * 14x + 3x * 14x) = 360
(140x + 42x2) = 360

Solving
140x + 42x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 140x + 42x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 140x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-180 + 70x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-180 + 70x + 21x2)' equal to zero and attempt to solve:

Simplifying
-180 + 70x + 21x2 = 0

Solving
-180 + 70x + 21x2 = 0

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

Divide each side by '21'.
-8.571428571 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + 3.333333333x + 8.571428571 + x2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + 3.333333333x + x2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 8.571428571
3.333333333x + x2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
3.333333333x + x2 = 8.571428571

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 8.571428571 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 8.571428571 + 2.777777779

Combine like terms: 8.571428571 + 2.777777779 = 11.34920635
2.777777779 + 3.333333333x + x2 = 11.34920635

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 11.34920635

Calculate the square root of the right side: 3.368858316

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.368858316 and -3.368858316.

Subproblem 1
x + 1.666666667 = 3.368858316

Simplifying
x + 1.666666667 = 3.368858316

Reorder the terms:
1.666666667 + x = 3.368858316

Solving
1.666666667 + x = 3.368858316

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 3.368858316 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 3.368858316 + -1.666666667
x = 3.368858316 + -1.666666667

Combine like terms: 3.368858316 + -1.666666667 = 1.702191649
x = 1.702191649

Simplifying
x = 1.702191649

Subproblem 2
x + 1.666666667 = -3.368858316

Simplifying
x + 1.666666667 = -3.368858316

Reorder the terms:
1.666666667 + x = -3.368858316

Solving
1.666666667 + x = -3.368858316

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -3.368858316 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -3.368858316 + -1.666666667
x = -3.368858316 + -1.666666667

Combine like terms: -3.368858316 + -1.666666667 = -5.035524983
x = -5.035524983

Simplifying
x = -5.035524983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.702191649, -5.035524983}
Solution
x = {1.702191649, -5.035524983}