4x(x-2)=5

Solution for 4x(x-2)=5 equation:

Simplifying
4x(x + -2) = 5

Reorder the terms:
4x(-2 + x) = 5
(-2 * 4x + x * 4x) = 5
(-8x + 4x2) = 5

Solving
-8x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -8x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -8x + 4x2 = 0

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

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

Simplifying
-1 + -2x = 0

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

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 2.5}