5x(x-6)=x-30

Solution for 5x(x-6)=x-30 equation:

Simplifying
5x(x + -6) = x + -30

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

Reorder the terms:
-30x + 5x2 = -30 + x

Solving
-30x + 5x2 = -30 + x

Solving for variable 'x'.

Reorder the terms:
30 + -30x + -1x + 5x2 = -30 + x + 30 + -1x

Combine like terms: -30x + -1x = -31x
30 + -31x + 5x2 = -30 + x + 30 + -1x

Reorder the terms:
30 + -31x + 5x2 = -30 + 30 + x + -1x

Combine like terms: -30 + 30 = 0
30 + -31x + 5x2 = 0 + x + -1x
30 + -31x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
30 + -31x + 5x2 = 0

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

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

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
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 = {1.2, 5}