(x-5)(10x+2)=0

Solution for (x-5)(10x+2)=0 equation:

Simplifying
(x + -5)(10x + 2) = 0

Reorder the terms:
(-5 + x)(10x + 2) = 0

Reorder the terms:
(-5 + x)(2 + 10x) = 0

Multiply (-5 + x) * (2 + 10x)
(-5(2 + 10x) + x(2 + 10x)) = 0
((2 * -5 + 10x * -5) + x(2 + 10x)) = 0
((-10 + -50x) + x(2 + 10x)) = 0
(-10 + -50x + (2 * x + 10x * x)) = 0
(-10 + -50x + (2x + 10x2)) = 0

Combine like terms: -50x + 2x = -48x
(-10 + -48x + 10x2) = 0

Solving
-10 + -48x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -24x + 5x2) = 0

Factor a trinomial.
2((-1 + -5x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

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

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

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 2
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
Solution
x = {-0.2, 5}