x^2-8x+45=8x-3

Solution for x^2-8x+45=8x-3 equation:

Simplifying
x2 + -8x + 45 = 8x + -3

Reorder the terms:
45 + -8x + x2 = 8x + -3

Reorder the terms:
45 + -8x + x2 = -3 + 8x

Solving
45 + -8x + x2 = -3 + 8x

Solving for variable 'x'.

Reorder the terms:
45 + 3 + -8x + -8x + x2 = -3 + 8x + 3 + -8x

Combine like terms: 45 + 3 = 48
48 + -8x + -8x + x2 = -3 + 8x + 3 + -8x

Combine like terms: -8x + -8x = -16x
48 + -16x + x2 = -3 + 8x + 3 + -8x

Reorder the terms:
48 + -16x + x2 = -3 + 3 + 8x + -8x

Combine like terms: -3 + 3 = 0
48 + -16x + x2 = 0 + 8x + -8x
48 + -16x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
48 + -16x + x2 = 0

Factor a trinomial.
(4 + -1x)(12 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 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 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {4, 12}