45x(9x)=30x+30

Solution for 45x(9x)=30x+30 equation:

Simplifying
45x(9x) = 30x + 30

Remove parenthesis around (9x)
45x * 9x = 30x + 30

Reorder the terms for easier multiplication:
45 * 9x * x = 30x + 30

Multiply 45 * 9
405x * x = 30x + 30

Multiply x * x
405x2 = 30x + 30

Reorder the terms:
405x2 = 30 + 30x

Solving
405x2 = 30 + 30x

Solving for variable 'x'.

Reorder the terms:
-30 + -30x + 405x2 = 30 + 30x + -30 + -30x

Reorder the terms:
-30 + -30x + 405x2 = 30 + -30 + 30x + -30x

Combine like terms: 30 + -30 = 0
-30 + -30x + 405x2 = 0 + 30x + -30x
-30 + -30x + 405x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-30 + -30x + 405x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-2 + -2x + 27x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-2 + -2x + 27x2)' equal to zero and attempt to solve:

Simplifying
-2 + -2x + 27x2 = 0

Solving
-2 + -2x + 27x2 = 0

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

Divide each side by '27'.
-0.07407407407 + -0.07407407407x + x2 = 0

Move the constant term to the right:

Add '0.07407407407' to each side of the equation.
-0.07407407407 + -0.07407407407x + 0.07407407407 + x2 = 0 + 0.07407407407

Reorder the terms:
-0.07407407407 + 0.07407407407 + -0.07407407407x + x2 = 0 + 0.07407407407

Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000
0.00000000000 + -0.07407407407x + x2 = 0 + 0.07407407407
-0.07407407407x + x2 = 0 + 0.07407407407

Combine like terms: 0 + 0.07407407407 = 0.07407407407
-0.07407407407x + x2 = 0.07407407407

The x term is -0.07407407407x.  Take half its coefficient (-0.03703703704).
Square it (0.001371742113) and add it to both sides.

Add '0.001371742113' to each side of the equation.
-0.07407407407x + 0.001371742113 + x2 = 0.07407407407 + 0.001371742113

Reorder the terms:
0.001371742113 + -0.07407407407x + x2 = 0.07407407407 + 0.001371742113

Combine like terms: 0.07407407407 + 0.001371742113 = 0.075445816183
0.001371742113 + -0.07407407407x + x2 = 0.075445816183

Factor a perfect square on the left side:
(x + -0.03703703704)(x + -0.03703703704) = 0.075445816183

Calculate the square root of the right side: 0.274674018

Break this problem into two subproblems by setting 
(x + -0.03703703704) equal to 0.274674018 and -0.274674018.

Subproblem 1
x + -0.03703703704 = 0.274674018

Simplifying
x + -0.03703703704 = 0.274674018

Reorder the terms:
-0.03703703704 + x = 0.274674018

Solving
-0.03703703704 + x = 0.274674018

Solving for variable 'x'.

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

Add '0.03703703704' to each side of the equation.
-0.03703703704 + 0.03703703704 + x = 0.274674018 + 0.03703703704

Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000
0.00000000000 + x = 0.274674018 + 0.03703703704
x = 0.274674018 + 0.03703703704

Combine like terms: 0.274674018 + 0.03703703704 = 0.31171105504
x = 0.31171105504

Simplifying
x = 0.31171105504

Subproblem 2
x + -0.03703703704 = -0.274674018

Simplifying
x + -0.03703703704 = -0.274674018

Reorder the terms:
-0.03703703704 + x = -0.274674018

Solving
-0.03703703704 + x = -0.274674018

Solving for variable 'x'.

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

Add '0.03703703704' to each side of the equation.
-0.03703703704 + 0.03703703704 + x = -0.274674018 + 0.03703703704

Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000
0.00000000000 + x = -0.274674018 + 0.03703703704
x = -0.274674018 + 0.03703703704

Combine like terms: -0.274674018 + 0.03703703704 = -0.23763698096
x = -0.23763698096

Simplifying
x = -0.23763698096

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.31171105504, -0.23763698096}
Solution
x = {0.31171105504, -0.23763698096}