(4x)(-1)(25-x)=70

Solution for (4x)(-1)(25-x)=70 equation:

Simplifying
(4x)(-1)(25 + -1x) = 70

Remove parenthesis around (4x)
4x(-1)(25 + -1x) = 70

Reorder the terms for easier multiplication:
4 * -1x(25 + -1x) = 70

Multiply 4 * -1
-4x(25 + -1x) = 70
(25 * -4x + -1x * -4x) = 70
(-100x + 4x2) = 70

Solving
-100x + 4x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + -100x + 4x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -50x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -50x + 2x2)' equal to zero and attempt to solve:

Simplifying
-35 + -50x + 2x2 = 0

Solving
-35 + -50x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + -25x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -25x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -25x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -25x + x2 = 0 + 17.5
-25x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-25x + x2 = 17.5

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = 17.5 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 17.5 + 156.25

Combine like terms: 17.5 + 156.25 = 173.75
156.25 + -25x + x2 = 173.75

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 173.75

Calculate the square root of the right side: 13.181426326

Break this problem into two subproblems by setting 
(x + -12.5) equal to 13.181426326 and -13.181426326.

Subproblem 1
x + -12.5 = 13.181426326

Simplifying
x + -12.5 = 13.181426326

Reorder the terms:
-12.5 + x = 13.181426326

Solving
-12.5 + x = 13.181426326

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 13.181426326 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 13.181426326 + 12.5
x = 13.181426326 + 12.5

Combine like terms: 13.181426326 + 12.5 = 25.681426326
x = 25.681426326

Simplifying
x = 25.681426326

Subproblem 2
x + -12.5 = -13.181426326

Simplifying
x + -12.5 = -13.181426326

Reorder the terms:
-12.5 + x = -13.181426326

Solving
-12.5 + x = -13.181426326

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -13.181426326 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -13.181426326 + 12.5
x = -13.181426326 + 12.5

Combine like terms: -13.181426326 + 12.5 = -0.681426326
x = -0.681426326

Simplifying
x = -0.681426326

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.681426326, -0.681426326}
Solution
x = {25.681426326, -0.681426326}