148+112+90+2x(2x+10)=540

Solution for 148+112+90+2x(2x+10)=540 equation:

Simplifying
148 + 112 + 90 + 2x(2x + 10) = 540

Reorder the terms:
148 + 112 + 90 + 2x(10 + 2x) = 540
148 + 112 + 90 + (10 * 2x + 2x * 2x) = 540
148 + 112 + 90 + (20x + 4x2) = 540

Combine like terms: 148 + 112 = 260
260 + 90 + 20x + 4x2 = 540

Combine like terms: 260 + 90 = 350
350 + 20x + 4x2 = 540

Solving
350 + 20x + 4x2 = 540

Solving for variable 'x'.

Reorder the terms:
350 + -540 + 20x + 4x2 = 540 + -540

Combine like terms: 350 + -540 = -190
-190 + 20x + 4x2 = 540 + -540

Combine like terms: 540 + -540 = 0
-190 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-95 + 10x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-95 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-95 + 10x + 2x2 = 0

Solving
-95 + 10x + 2x2 = 0

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

Divide each side by '2'.
-47.5 + 5x + x2 = 0

Move the constant term to the right:

Add '47.5' to each side of the equation.
-47.5 + 5x + 47.5 + x2 = 0 + 47.5

Reorder the terms:
-47.5 + 47.5 + 5x + x2 = 0 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + 5x + x2 = 0 + 47.5
5x + x2 = 0 + 47.5

Combine like terms: 0 + 47.5 = 47.5
5x + x2 = 47.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 47.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 47.5 + 6.25

Combine like terms: 47.5 + 6.25 = 53.75
6.25 + 5x + x2 = 53.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 53.75

Calculate the square root of the right side: 7.331439149

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.331439149 and -7.331439149.

Subproblem 1
x + 2.5 = 7.331439149

Simplifying
x + 2.5 = 7.331439149

Reorder the terms:
2.5 + x = 7.331439149

Solving
2.5 + x = 7.331439149

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 7.331439149 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.331439149 + -2.5
x = 7.331439149 + -2.5

Combine like terms: 7.331439149 + -2.5 = 4.831439149
x = 4.831439149

Simplifying
x = 4.831439149

Subproblem 2
x + 2.5 = -7.331439149

Simplifying
x + 2.5 = -7.331439149

Reorder the terms:
2.5 + x = -7.331439149

Solving
2.5 + x = -7.331439149

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -7.331439149 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.331439149 + -2.5
x = -7.331439149 + -2.5

Combine like terms: -7.331439149 + -2.5 = -9.831439149
x = -9.831439149

Simplifying
x = -9.831439149

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.831439149, -9.831439149}
Solution
x = {4.831439149, -9.831439149}