690=x*(x+31)

Solution for 690=x*(x+31) equation:

Simplifying
690 = x(x + 31)

Reorder the terms:
690 = x(31 + x)
690 = (31 * x + x * x)
690 = (31x + x2)

Solving
690 = 31x + x2

Solving for variable 'x'.

Reorder the terms:
690 + -31x + -1x2 = 31x + -31x + x2 + -1x2

Combine like terms: 31x + -31x = 0
690 + -31x + -1x2 = 0 + x2 + -1x2
690 + -31x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
690 + -31x + -1x2 = 0

Factor a trinomial.
(15 + -1x)(46 + x) = 0

Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Subproblem 2
Set the factor '(46 + x)' equal to zero and attempt to solve:

Simplifying
46 + x = 0

Solving
46 + x = 0

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

Add '-46' to each side of the equation.
46 + -46 + x = 0 + -46

Combine like terms: 46 + -46 = 0
0 + x = 0 + -46
x = 0 + -46

Combine like terms: 0 + -46 = -46
x = -46

Simplifying
x = -46
Solution
x = {15, -46}