4r^2-4r+1=144

Solution for 4r^2-4r+1=144 equation:

Simplifying
4r2 + -4r + 1 = 144

Reorder the terms:
1 + -4r + 4r2 = 144

Solving
1 + -4r + 4r2 = 144

Solving for variable 'r'.

Reorder the terms:
1 + -144 + -4r + 4r2 = 144 + -144

Combine like terms: 1 + -144 = -143
-143 + -4r + 4r2 = 144 + -144

Combine like terms: 144 + -144 = 0
-143 + -4r + 4r2 = 0

Factor a trinomial.
(-11 + -2r)(13 + -2r) = 0

Subproblem 1
Set the factor '(-11 + -2r)' equal to zero and attempt to solve:

Simplifying
-11 + -2r = 0

Solving
-11 + -2r = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2r = 0 + 11
-2r = 0 + 11

Combine like terms: 0 + 11 = 11
-2r = 11

Divide each side by '-2'.
r = -5.5

Simplifying
r = -5.5
Subproblem 2
Set the factor '(13 + -2r)' equal to zero and attempt to solve:

Simplifying
13 + -2r = 0

Solving
13 + -2r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2r = 0 + -13
-2r = 0 + -13

Combine like terms: 0 + -13 = -13
-2r = -13

Divide each side by '-2'.
r = 6.5

Simplifying
r = 6.5
Solution
r = {-5.5, 6.5}