(5x-2)(6x-3)=x

Solution for (5x-2)(6x-3)=x equation:

Simplifying
(5x + -2)(6x + -3) = x

Reorder the terms:
(-2 + 5x)(6x + -3) = x

Reorder the terms:
(-2 + 5x)(-3 + 6x) = x

Multiply (-2 + 5x) * (-3 + 6x)
(-2(-3 + 6x) + 5x * (-3 + 6x)) = x
((-3 * -2 + 6x * -2) + 5x * (-3 + 6x)) = x
((6 + -12x) + 5x * (-3 + 6x)) = x
(6 + -12x + (-3 * 5x + 6x * 5x)) = x
(6 + -12x + (-15x + 30x2)) = x

Combine like terms: -12x + -15x = -27x
(6 + -27x + 30x2) = x

Solving
6 + -27x + 30x2 = x

Solving for variable 'x'.

Reorder the terms:
6 + -27x + -1x + 30x2 = x + -1x

Combine like terms: -27x + -1x = -28x
6 + -28x + 30x2 = x + -1x

Combine like terms: x + -1x = 0
6 + -28x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -14x + 15x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0.3333333333, 0.6}