4x^2-22x=-10

Solution for 4x^2-22x=-10 equation:

Simplifying
4x2 + -22x = -10

Reorder the terms:
-22x + 4x2 = -10

Solving
-22x + 4x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + -22x + 4x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -11x + 2x2) = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
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 = {0.5, 5}