(2x-7)(0.3-x)=0

Solution for (2x-7)(0.3-x)=0 equation:

Simplifying
(2x + -7)(0.3 + -1x) = 0

Reorder the terms:
(-7 + 2x)(0.3 + -1x) = 0

Multiply (-7 + 2x) * (0.3 + -1x)
(-7(0.3 + -1x) + 2x * (0.3 + -1x)) = 0
((0.3 * -7 + -1x * -7) + 2x * (0.3 + -1x)) = 0
((-2.1 + 7x) + 2x * (0.3 + -1x)) = 0
(-2.1 + 7x + (0.3 * 2x + -1x * 2x)) = 0
(-2.1 + 7x + (0.6x + -2x2)) = 0

Combine like terms: 7x + 0.6x = 7.6x
(-2.1 + 7.6x + -2x2) = 0

Solving
-2.1 + 7.6x + -2x2 = 0

Solving for variable 'x'.

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

Divide each side by '-2'.
1.05 + -3.8x + x2 = 0

Move the constant term to the right:

Add '-1.05' to each side of the equation.
1.05 + -3.8x + -1.05 + x2 = 0 + -1.05

Reorder the terms:
1.05 + -1.05 + -3.8x + x2 = 0 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + -3.8x + x2 = 0 + -1.05
-3.8x + x2 = 0 + -1.05

Combine like terms: 0 + -1.05 = -1.05
-3.8x + x2 = -1.05

The x term is -3.8x.  Take half its coefficient (-1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
-3.8x + 3.61 + x2 = -1.05 + 3.61

Reorder the terms:
3.61 + -3.8x + x2 = -1.05 + 3.61

Combine like terms: -1.05 + 3.61 = 2.56
3.61 + -3.8x + x2 = 2.56

Factor a perfect square on the left side:
(x + -1.9)(x + -1.9) = 2.56

Calculate the square root of the right side: 1.6

Break this problem into two subproblems by setting 
(x + -1.9) equal to 1.6 and -1.6.

Subproblem 1
x + -1.9 = 1.6

Simplifying
x + -1.9 = 1.6

Reorder the terms:
-1.9 + x = 1.6

Solving
-1.9 + x = 1.6

Solving for variable 'x'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + x = 1.6 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + x = 1.6 + 1.9
x = 1.6 + 1.9

Combine like terms: 1.6 + 1.9 = 3.5
x = 3.5

Simplifying
x = 3.5

Subproblem 2
x + -1.9 = -1.6

Simplifying
x + -1.9 = -1.6

Reorder the terms:
-1.9 + x = -1.6

Solving
-1.9 + x = -1.6

Solving for variable 'x'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + x = -1.6 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + x = -1.6 + 1.9
x = -1.6 + 1.9

Combine like terms: -1.6 + 1.9 = 0.3
x = 0.3

Simplifying
x = 0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, 0.3}