4X^2+20X-5(0.8X+4)=0

Solution for 4X^2+20X-5(0.8X+4)=0 equation:

Simplifying
4X2 + 20X + -5(0.8X + 4) = 0

Reorder the terms:
4X2 + 20X + -5(4 + 0.8X) = 0
4X2 + 20X + (4 * -5 + 0.8X * -5) = 0
4X2 + 20X + (-20 + -4X) = 0

Reorder the terms:
-20 + 20X + -4X + 4X2 = 0

Combine like terms: 20X + -4X = 16X
-20 + 16X + 4X2 = 0

Solving
-20 + 16X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 4X + X2) = 0

Factor a trinomial.
4((-5 + -1X)(1 + -1X)) = 0

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

Simplifying
-5 + -1X = 0

Solving
-5 + -1X = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1X = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1X = 0 + 5
-1X = 0 + 5

Combine like terms: 0 + 5 = 5
-1X = 5

Divide each side by '-1'.
X = -5

Simplifying
X = -5
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-5, 1}