(x-5)(5x+30)=0

Solution for (x-5)(5x+30)=0 equation:

Simplifying
(x + -5)(5x + 30) = 0

Reorder the terms:
(-5 + x)(5x + 30) = 0

Reorder the terms:
(-5 + x)(30 + 5x) = 0

Multiply (-5 + x) * (30 + 5x)
(-5(30 + 5x) + x(30 + 5x)) = 0
((30 * -5 + 5x * -5) + x(30 + 5x)) = 0
((-150 + -25x) + x(30 + 5x)) = 0
(-150 + -25x + (30 * x + 5x * x)) = 0
(-150 + -25x + (30x + 5x2)) = 0

Combine like terms: -25x + 30x = 5x
(-150 + 5x + 5x2) = 0

Solving
-150 + 5x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-30 + x + x2) = 0

Factor a trinomial.
5((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 5}