x(2x+1)=2(10-x)

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Solution for x(2x+1)=2(10-x) equation: 


Simplifying
x(2x + 1) = 2(10 + -1x)

Reorder the terms:
x(1 + 2x) = 2(10 + -1x)
(1 * x + 2x * x) = 2(10 + -1x)
(1x + 2x2) = 2(10 + -1x)
1x + 2x2 = (10 * 2 + -1x * 2)
1x + 2x2 = (20 + -2x)

Solving
1x + 2x2 = 20 + -2x

Solving for variable 'x'.

Reorder the terms:
-20 + 1x + 2x + 2x2 = 20 + -2x + -20 + 2x

Combine like terms: 1x + 2x = 3x
-20 + 3x + 2x2 = 20 + -2x + -20 + 2x

Reorder the terms:
-20 + 3x + 2x2 = 20 + -20 + -2x + 2x

Combine like terms: 20 + -20 = 0
-20 + 3x + 2x2 = 0 + -2x + 2x
-20 + 3x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-20 + 3x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 2.5}

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