x(5x-1)-15(x-1)=12

Solution for x(5x-1)-15(x-1)=12 equation:

Simplifying
x(5x + -1) + -15(x + -1) = 12

Reorder the terms:
x(-1 + 5x) + -15(x + -1) = 12
(-1 * x + 5x * x) + -15(x + -1) = 12
(-1x + 5x2) + -15(x + -1) = 12

Reorder the terms:
-1x + 5x2 + -15(-1 + x) = 12
-1x + 5x2 + (-1 * -15 + x * -15) = 12
-1x + 5x2 + (15 + -15x) = 12

Reorder the terms:
15 + -1x + -15x + 5x2 = 12

Combine like terms: -1x + -15x = -16x
15 + -16x + 5x2 = 12

Solving
15 + -16x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
15 + -12 + -16x + 5x2 = 12 + -12

Combine like terms: 15 + -12 = 3
3 + -16x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
3 + -16x + 5x2 = 0

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

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
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 = {0.2, 3}