2x^2-13x+21=1

Solution for 2x^2-13x+21=1 equation:

Simplifying
2x2 + -13x + 21 = 1

Reorder the terms:
21 + -13x + 2x2 = 1

Solving
21 + -13x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
21 + -1 + -13x + 2x2 = 1 + -1

Combine like terms: 21 + -1 = 20
20 + -13x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
20 + -13x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(4 + -1x) = 0

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
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
Solution
x = {2.5, 4}