7x-3(1-x)=x(5x-11)

Solution for 7x-3(1-x)=x(5x-11) equation:

Simplifying
7x + -3(1 + -1x) = x(5x + -11)
7x + (1 * -3 + -1x * -3) = x(5x + -11)
7x + (-3 + 3x) = x(5x + -11)

Reorder the terms:
-3 + 7x + 3x = x(5x + -11)

Combine like terms: 7x + 3x = 10x
-3 + 10x = x(5x + -11)

Reorder the terms:
-3 + 10x = x(-11 + 5x)
-3 + 10x = (-11 * x + 5x * x)
-3 + 10x = (-11x + 5x2)

Solving
-3 + 10x = -11x + 5x2

Solving for variable 'x'.

Combine like terms: 10x + 11x = 21x
-3 + 21x + -5x2 = -11x + 5x2 + 11x + -5x2

Reorder the terms:
-3 + 21x + -5x2 = -11x + 11x + 5x2 + -5x2

Combine like terms: -11x + 11x = 0
-3 + 21x + -5x2 = 0 + 5x2 + -5x2
-3 + 21x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-3 + 21x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -4.2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -4.2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -4.2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -4.2x + x2 = 0 + -0.6
-4.2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-4.2x + x2 = -0.6

The x term is -4.2x.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2x + 4.41 + x2 = -0.6 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = -0.6 + 4.41

Combine like terms: -0.6 + 4.41 = 3.81
4.41 + -4.2x + x2 = 3.81

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 3.81

Calculate the square root of the right side: 1.95192213

Break this problem into two subproblems by setting 
(x + -2.1) equal to 1.95192213 and -1.95192213.

Subproblem 1
x + -2.1 = 1.95192213

Simplifying
x + -2.1 = 1.95192213

Reorder the terms:
-2.1 + x = 1.95192213

Solving
-2.1 + x = 1.95192213

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = 1.95192213 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 1.95192213 + 2.1
x = 1.95192213 + 2.1

Combine like terms: 1.95192213 + 2.1 = 4.05192213
x = 4.05192213

Simplifying
x = 4.05192213

Subproblem 2
x + -2.1 = -1.95192213

Simplifying
x + -2.1 = -1.95192213

Reorder the terms:
-2.1 + x = -1.95192213

Solving
-2.1 + x = -1.95192213

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = -1.95192213 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -1.95192213 + 2.1
x = -1.95192213 + 2.1

Combine like terms: -1.95192213 + 2.1 = 0.14807787
x = 0.14807787

Simplifying
x = 0.14807787

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.05192213, 0.14807787}