4x(5x-3)=28

Solution for 4x(5x-3)=28 equation:

Simplifying
4x(5x + -3) = 28

Reorder the terms:
4x(-3 + 5x) = 28
(-3 * 4x + 5x * 4x) = 28
(-12x + 20x2) = 28

Solving
-12x + 20x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + -12x + 20x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + -12x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + -3x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-7 + -3x + 5x2 = 0

Solving
-7 + -3x + 5x2 = 0

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

Divide each side by '5'.
-1.4 + -0.6x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -0.6x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -0.6x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -0.6x + x2 = 0 + 1.4
-0.6x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-0.6x + x2 = 1.4

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 1.4 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 1.4 + 0.09

Combine like terms: 1.4 + 0.09 = 1.49
0.09 + -0.6x + x2 = 1.49

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 1.49

Calculate the square root of the right side: 1.220655562

Break this problem into two subproblems by setting 
(x + -0.3) equal to 1.220655562 and -1.220655562.

Subproblem 1
x + -0.3 = 1.220655562

Simplifying
x + -0.3 = 1.220655562

Reorder the terms:
-0.3 + x = 1.220655562

Solving
-0.3 + x = 1.220655562

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 1.220655562 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 1.220655562 + 0.3
x = 1.220655562 + 0.3

Combine like terms: 1.220655562 + 0.3 = 1.520655562
x = 1.520655562

Simplifying
x = 1.520655562

Subproblem 2
x + -0.3 = -1.220655562

Simplifying
x + -0.3 = -1.220655562

Reorder the terms:
-0.3 + x = -1.220655562

Solving
-0.3 + x = -1.220655562

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -1.220655562 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -1.220655562 + 0.3
x = -1.220655562 + 0.3

Combine like terms: -1.220655562 + 0.3 = -0.920655562
x = -0.920655562

Simplifying
x = -0.920655562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.520655562, -0.920655562}
Solution
x = {1.520655562, -0.920655562}