x^2-6x+10=2x+3

Solution for x^2-6x+10=2x+3 equation:

Simplifying
x2 + -6x + 10 = 2x + 3

Reorder the terms:
10 + -6x + x2 = 2x + 3

Reorder the terms:
10 + -6x + x2 = 3 + 2x

Solving
10 + -6x + x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
10 + -3 + -6x + -2x + x2 = 3 + 2x + -3 + -2x

Combine like terms: 10 + -3 = 7
7 + -6x + -2x + x2 = 3 + 2x + -3 + -2x

Combine like terms: -6x + -2x = -8x
7 + -8x + x2 = 3 + 2x + -3 + -2x

Reorder the terms:
7 + -8x + x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
7 + -8x + x2 = 0 + 2x + -2x
7 + -8x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
7 + -8x + x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}