45=(12+x)*x

Solution for 45=(12+x)*x equation:

Simplifying
45 = (12 + x) * x

Reorder the terms for easier multiplication:
45 = x(12 + x)
45 = (12 * x + x * x)
45 = (12x + x2)

Solving
45 = 12x + x2

Solving for variable 'x'.

Reorder the terms:
45 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
45 + -12x + -1x2 = 0 + x2 + -1x2
45 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + -12x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(15 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

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

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

Simplifying
x = -15
Solution
x = {3, -15}