x=(7x+15)(10x+12)

Solution for x=(7x+15)(10x+12) equation:

Simplifying
x = (7x + 15)(10x + 12)

Reorder the terms:
x = (15 + 7x)(10x + 12)

Reorder the terms:
x = (15 + 7x)(12 + 10x)

Multiply (15 + 7x) * (12 + 10x)
x = (15(12 + 10x) + 7x * (12 + 10x))
x = ((12 * 15 + 10x * 15) + 7x * (12 + 10x))
x = ((180 + 150x) + 7x * (12 + 10x))
x = (180 + 150x + (12 * 7x + 10x * 7x))
x = (180 + 150x + (84x + 70x2))

Combine like terms: 150x + 84x = 234x
x = (180 + 234x + 70x2)

Solving
x = 180 + 234x + 70x2

Solving for variable 'x'.

Reorder the terms:
-180 + x + -234x + -70x2 = 180 + 234x + 70x2 + -180 + -234x + -70x2

Combine like terms: x + -234x = -233x
-180 + -233x + -70x2 = 180 + 234x + 70x2 + -180 + -234x + -70x2

Reorder the terms:
-180 + -233x + -70x2 = 180 + -180 + 234x + -234x + 70x2 + -70x2

Combine like terms: 180 + -180 = 0
-180 + -233x + -70x2 = 0 + 234x + -234x + 70x2 + -70x2
-180 + -233x + -70x2 = 234x + -234x + 70x2 + -70x2

Combine like terms: 234x + -234x = 0
-180 + -233x + -70x2 = 0 + 70x2 + -70x2
-180 + -233x + -70x2 = 70x2 + -70x2

Combine like terms: 70x2 + -70x2 = 0
-180 + -233x + -70x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(180 + 233x + 70x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(180 + 233x + 70x2)' equal to zero and attempt to solve:

Simplifying
180 + 233x + 70x2 = 0

Solving
180 + 233x + 70x2 = 0

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

Divide each side by '70'.
2.571428571 + 3.328571429x + x2 = 0.0

Move the constant term to the right:

Add '-2.571428571' to each side of the equation.
2.571428571 + 3.328571429x + -2.571428571 + x2 = 0.0 + -2.571428571

Reorder the terms:
2.571428571 + -2.571428571 + 3.328571429x + x2 = 0.0 + -2.571428571

Combine like terms: 2.571428571 + -2.571428571 = 0.000000000
0.000000000 + 3.328571429x + x2 = 0.0 + -2.571428571
3.328571429x + x2 = 0.0 + -2.571428571

Combine like terms: 0.0 + -2.571428571 = -2.571428571
3.328571429x + x2 = -2.571428571

The x term is 3.328571429x.  Take half its coefficient (1.664285715).
Square it (2.769846941) and add it to both sides.

Add '2.769846941' to each side of the equation.
3.328571429x + 2.769846941 + x2 = -2.571428571 + 2.769846941

Reorder the terms:
2.769846941 + 3.328571429x + x2 = -2.571428571 + 2.769846941

Combine like terms: -2.571428571 + 2.769846941 = 0.19841837
2.769846941 + 3.328571429x + x2 = 0.19841837

Factor a perfect square on the left side:
(x + 1.664285715)(x + 1.664285715) = 0.19841837

Calculate the square root of the right side: 0.445441769

Break this problem into two subproblems by setting 
(x + 1.664285715) equal to 0.445441769 and -0.445441769.

Subproblem 1
x + 1.664285715 = 0.445441769

Simplifying
x + 1.664285715 = 0.445441769

Reorder the terms:
1.664285715 + x = 0.445441769

Solving
1.664285715 + x = 0.445441769

Solving for variable 'x'.

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

Add '-1.664285715' to each side of the equation.
1.664285715 + -1.664285715 + x = 0.445441769 + -1.664285715

Combine like terms: 1.664285715 + -1.664285715 = 0.000000000
0.000000000 + x = 0.445441769 + -1.664285715
x = 0.445441769 + -1.664285715

Combine like terms: 0.445441769 + -1.664285715 = -1.218843946
x = -1.218843946

Simplifying
x = -1.218843946

Subproblem 2
x + 1.664285715 = -0.445441769

Simplifying
x + 1.664285715 = -0.445441769

Reorder the terms:
1.664285715 + x = -0.445441769

Solving
1.664285715 + x = -0.445441769

Solving for variable 'x'.

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

Add '-1.664285715' to each side of the equation.
1.664285715 + -1.664285715 + x = -0.445441769 + -1.664285715

Combine like terms: 1.664285715 + -1.664285715 = 0.000000000
0.000000000 + x = -0.445441769 + -1.664285715
x = -0.445441769 + -1.664285715

Combine like terms: -0.445441769 + -1.664285715 = -2.109727484
x = -2.109727484

Simplifying
x = -2.109727484

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.218843946, -2.109727484}
Solution
x = {-1.218843946, -2.109727484}