x(2x-1)-15=0

Solution for x(2x-1)-15=0 equation:

Simplifying
x(2x + -1) + -15 = 0

Reorder the terms:
x(-1 + 2x) + -15 = 0
(-1 * x + 2x * x) + -15 = 0
(-1x + 2x2) + -15 = 0

Reorder the terms:
-15 + -1x + 2x2 = 0

Solving
-15 + -1x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
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 = {-2.5, 3}