3x(2-x)+x(x+1)=5

Solution for 3x(2-x)+x(x+1)=5 equation:

Simplifying
3x(2 + -1x) + x(x + 1) = 5
(2 * 3x + -1x * 3x) + x(x + 1) = 5
(6x + -3x2) + x(x + 1) = 5

Reorder the terms:
6x + -3x2 + x(1 + x) = 5
6x + -3x2 + (1 * x + x * x) = 5
6x + -3x2 + (1x + x2) = 5

Reorder the terms:
6x + 1x + -3x2 + x2 = 5

Combine like terms: 6x + 1x = 7x
7x + -3x2 + x2 = 5

Combine like terms: -3x2 + x2 = -2x2
7x + -2x2 = 5

Solving
7x + -2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 7x + -2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 7x + -2x2 = 0

Factor a trinomial.
(-5 + 2x)(1 + -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 '(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
Solution
x = {2.5, 1}