x(2x-3)=5

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

Simplifying
x(2x + -3) = 5

Reorder the terms:
x(-3 + 2x) = 5
(-3 * x + 2x * x) = 5
(-3x + 2x2) = 5

Solving
-3x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -3x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -3x + 2x2 = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 2.5}