84=x(5+x)

Solution for 84=x(5+x) equation:

Simplifying
84 = x(5 + x)
84 = (5 * x + x * x)
84 = (5x + x2)

Solving
84 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
84 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
84 + -5x + -1x2 = 0 + x2 + -1x2
84 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
84 + -5x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(12 + x) = 0

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {7, -12}