5x(x-3)+25(x-3)=0

Solution for 5x(x-3)+25(x-3)=0 equation:

Simplifying
5x(x + -3) + 25(x + -3) = 0

Reorder the terms:
5x(-3 + x) + 25(x + -3) = 0
(-3 * 5x + x * 5x) + 25(x + -3) = 0
(-15x + 5x2) + 25(x + -3) = 0

Reorder the terms:
-15x + 5x2 + 25(-3 + x) = 0
-15x + 5x2 + (-3 * 25 + x * 25) = 0
-15x + 5x2 + (-75 + 25x) = 0

Reorder the terms:
-75 + -15x + 25x + 5x2 = 0

Combine like terms: -15x + 25x = 10x
-75 + 10x + 5x2 = 0

Solving
-75 + 10x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + 2x + x2) = 0

Factor a trinomial.
5((-5 + -1x)(3 + -1x)) = 0

Ignore the factor 5.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5, 3}