(11x+3)(20x-25)=35

Solution for (11x+3)(20x-25)=35 equation:

Simplifying
(11x + 3)(20x + -25) = 35

Reorder the terms:
(3 + 11x)(20x + -25) = 35

Reorder the terms:
(3 + 11x)(-25 + 20x) = 35

Multiply (3 + 11x) * (-25 + 20x)
(3(-25 + 20x) + 11x * (-25 + 20x)) = 35
((-25 * 3 + 20x * 3) + 11x * (-25 + 20x)) = 35
((-75 + 60x) + 11x * (-25 + 20x)) = 35
(-75 + 60x + (-25 * 11x + 20x * 11x)) = 35
(-75 + 60x + (-275x + 220x2)) = 35

Combine like terms: 60x + -275x = -215x
(-75 + -215x + 220x2) = 35

Solving
-75 + -215x + 220x2 = 35

Solving for variable 'x'.

Reorder the terms:
-75 + -35 + -215x + 220x2 = 35 + -35

Combine like terms: -75 + -35 = -110
-110 + -215x + 220x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-110 + -215x + 220x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-22 + -43x + 44x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-22 + -43x + 44x2)' equal to zero and attempt to solve:

Simplifying
-22 + -43x + 44x2 = 0

Solving
-22 + -43x + 44x2 = 0

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

Divide each side by '44'.
-0.5 + -0.9772727273x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.9772727273x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.9772727273x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.9772727273x + x2 = 0 + 0.5
-0.9772727273x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.9772727273x + x2 = 0.5

The x term is -0.9772727273x.  Take half its coefficient (-0.4886363637).
Square it (0.2387654959) and add it to both sides.

Add '0.2387654959' to each side of the equation.
-0.9772727273x + 0.2387654959 + x2 = 0.5 + 0.2387654959

Reorder the terms:
0.2387654959 + -0.9772727273x + x2 = 0.5 + 0.2387654959

Combine like terms: 0.5 + 0.2387654959 = 0.7387654959
0.2387654959 + -0.9772727273x + x2 = 0.7387654959

Factor a perfect square on the left side:
(x + -0.4886363637)(x + -0.4886363637) = 0.7387654959

Calculate the square root of the right side: 0.859514686

Break this problem into two subproblems by setting 
(x + -0.4886363637) equal to 0.859514686 and -0.859514686.

Subproblem 1
x + -0.4886363637 = 0.859514686

Simplifying
x + -0.4886363637 = 0.859514686

Reorder the terms:
-0.4886363637 + x = 0.859514686

Solving
-0.4886363637 + x = 0.859514686

Solving for variable 'x'.

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

Add '0.4886363637' to each side of the equation.
-0.4886363637 + 0.4886363637 + x = 0.859514686 + 0.4886363637

Combine like terms: -0.4886363637 + 0.4886363637 = 0.0000000000
0.0000000000 + x = 0.859514686 + 0.4886363637
x = 0.859514686 + 0.4886363637

Combine like terms: 0.859514686 + 0.4886363637 = 1.3481510497
x = 1.3481510497

Simplifying
x = 1.3481510497

Subproblem 2
x + -0.4886363637 = -0.859514686

Simplifying
x + -0.4886363637 = -0.859514686

Reorder the terms:
-0.4886363637 + x = -0.859514686

Solving
-0.4886363637 + x = -0.859514686

Solving for variable 'x'.

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

Add '0.4886363637' to each side of the equation.
-0.4886363637 + 0.4886363637 + x = -0.859514686 + 0.4886363637

Combine like terms: -0.4886363637 + 0.4886363637 = 0.0000000000
0.0000000000 + x = -0.859514686 + 0.4886363637
x = -0.859514686 + 0.4886363637

Combine like terms: -0.859514686 + 0.4886363637 = -0.3708783223
x = -0.3708783223

Simplifying
x = -0.3708783223

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3481510497, -0.3708783223}
Solution
x = {1.3481510497, -0.3708783223}