x(x-4)=45

Solution for x(x-4)=45 equation:

Simplifying
x(x + -4) = 45

Reorder the terms:
x(-4 + x) = 45
(-4 * x + x * x) = 45
(-4x + x2) = 45

Solving
-4x + x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -4x + x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-5, 9}