(2x-4)(5-21x)=0

Solution for (2x-4)(5-21x)=0 equation:

Simplifying
(2x + -4)(5 + -21x) = 0

Reorder the terms:
(-4 + 2x)(5 + -21x) = 0

Multiply (-4 + 2x) * (5 + -21x)
(-4(5 + -21x) + 2x * (5 + -21x)) = 0
((5 * -4 + -21x * -4) + 2x * (5 + -21x)) = 0
((-20 + 84x) + 2x * (5 + -21x)) = 0
(-20 + 84x + (5 * 2x + -21x * 2x)) = 0
(-20 + 84x + (10x + -42x2)) = 0

Combine like terms: 84x + 10x = 94x
(-20 + 94x + -42x2) = 0

Solving
-20 + 94x + -42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 47x + -21x2) = 0

Factor a trinomial.
2((-2 + x)(5 + -21x)) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(5 + -21x)' equal to zero and attempt to solve:

Simplifying
5 + -21x = 0

Solving
5 + -21x = 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 + -21x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -21x = 0 + -5
-21x = 0 + -5

Combine like terms: 0 + -5 = -5
-21x = -5

Divide each side by '-21'.
x = 0.2380952381

Simplifying
x = 0.2380952381
Solution
x = {2, 0.2380952381}