4x^2-24x+21=1

Solution for 4x^2-24x+21=1 equation:

Simplifying
4x2 + -24x + 21 = 1

Reorder the terms:
21 + -24x + 4x2 = 1

Solving
21 + -24x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
21 + -1 + -24x + 4x2 = 1 + -1

Combine like terms: 21 + -1 = 20
20 + -24x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
20 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -6x + x2) = 0

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

Ignore the factor 4.
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 '(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
Solution
x = {1, 5}