x(9+x)=4(2x+5)

Solution for x(9+x)=4(2x+5) equation:

Simplifying
x(9 + x) = 4(2x + 5)
(9 * x + x * x) = 4(2x + 5)
(9x + x2) = 4(2x + 5)

Reorder the terms:
9x + x2 = 4(5 + 2x)
9x + x2 = (5 * 4 + 2x * 4)
9x + x2 = (20 + 8x)

Solving
9x + x2 = 20 + 8x

Solving for variable 'x'.

Reorder the terms:
-20 + 9x + -8x + x2 = 20 + 8x + -20 + -8x

Combine like terms: 9x + -8x = 1x
-20 + 1x + x2 = 20 + 8x + -20 + -8x

Reorder the terms:
-20 + 1x + x2 = 20 + -20 + 8x + -8x

Combine like terms: 20 + -20 = 0
-20 + 1x + x2 = 0 + 8x + -8x
-20 + 1x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-20 + 1x + x2 = 0

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

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
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
Solution
x = {-5, 4}