4h^2-2h+1=7

Solution for 4h^2-2h+1=7 equation:

Simplifying
4h2 + -2h + 1 = 7

Reorder the terms:
1 + -2h + 4h2 = 7

Solving
1 + -2h + 4h2 = 7

Solving for variable 'h'.

Reorder the terms:
1 + -7 + -2h + 4h2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + -2h + 4h2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + -2h + 4h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1h + 2h2) = 0

Factor a trinomial.
2((-1 + -1h)(3 + -2h)) = 0

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

Simplifying
-1 + -1h = 0

Solving
-1 + -1h = 0

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

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

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

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

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

Simplifying
h = -1
Subproblem 2
Set the factor '(3 + -2h)' equal to zero and attempt to solve:

Simplifying
3 + -2h = 0

Solving
3 + -2h = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2h = 0 + -3
-2h = 0 + -3

Combine like terms: 0 + -3 = -3
-2h = -3

Divide each side by '-2'.
h = 1.5

Simplifying
h = 1.5
Solution
h = {-1, 1.5}