x^2-8x+27=5x-3

Solution for x^2-8x+27=5x-3 equation:

Simplifying
x2 + -8x + 27 = 5x + -3

Reorder the terms:
27 + -8x + x2 = 5x + -3

Reorder the terms:
27 + -8x + x2 = -3 + 5x

Solving
27 + -8x + x2 = -3 + 5x

Solving for variable 'x'.

Reorder the terms:
27 + 3 + -8x + -5x + x2 = -3 + 5x + 3 + -5x

Combine like terms: 27 + 3 = 30
30 + -8x + -5x + x2 = -3 + 5x + 3 + -5x

Combine like terms: -8x + -5x = -13x
30 + -13x + x2 = -3 + 5x + 3 + -5x

Reorder the terms:
30 + -13x + x2 = -3 + 3 + 5x + -5x

Combine like terms: -3 + 3 = 0
30 + -13x + x2 = 0 + 5x + -5x
30 + -13x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -1x) = 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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}