2x(x-5)=6(x-5)

Solution for 2x(x-5)=6(x-5) equation:

Simplifying
2x(x + -5) = 6(x + -5)

Reorder the terms:
2x(-5 + x) = 6(x + -5)
(-5 * 2x + x * 2x) = 6(x + -5)
(-10x + 2x2) = 6(x + -5)

Reorder the terms:
-10x + 2x2 = 6(-5 + x)
-10x + 2x2 = (-5 * 6 + x * 6)
-10x + 2x2 = (-30 + 6x)

Solving
-10x + 2x2 = -30 + 6x

Solving for variable 'x'.

Reorder the terms:
30 + -10x + -6x + 2x2 = -30 + 6x + 30 + -6x

Combine like terms: -10x + -6x = -16x
30 + -16x + 2x2 = -30 + 6x + 30 + -6x

Reorder the terms:
30 + -16x + 2x2 = -30 + 30 + 6x + -6x

Combine like terms: -30 + 30 = 0
30 + -16x + 2x2 = 0 + 6x + -6x
30 + -16x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
30 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -8x + x2) = 0

Factor a trinomial.
2((3 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {3, 5}