4(5-x)(8x+2)=0

Solution for 4(5-x)(8x+2)=0 equation:

Simplifying
4(5 + -1x)(8x + 2) = 0

Reorder the terms:
4(5 + -1x)(2 + 8x) = 0

Multiply (5 + -1x) * (2 + 8x)
4(5(2 + 8x) + -1x * (2 + 8x)) = 0
4((2 * 5 + 8x * 5) + -1x * (2 + 8x)) = 0
4((10 + 40x) + -1x * (2 + 8x)) = 0
4(10 + 40x + (2 * -1x + 8x * -1x)) = 0
4(10 + 40x + (-2x + -8x2)) = 0

Combine like terms: 40x + -2x = 38x
4(10 + 38x + -8x2) = 0
(10 * 4 + 38x * 4 + -8x2 * 4) = 0
(40 + 152x + -32x2) = 0

Solving
40 + 152x + -32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 19x + -4x2) = 0

Factor a trinomial.
8((5 + -1x)(1 + 4x)) = 0

Ignore the factor 8.
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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {5, -0.25}