100(1+r)(1+r)=144

Solution for 100(1+r)(1+r)=144 equation:

Simplifying
100(1 + r)(1 + r) = 144

Multiply (1 + r) * (1 + r)
100(1(1 + r) + r(1 + r)) = 144
100((1 * 1 + r * 1) + r(1 + r)) = 144
100((1 + 1r) + r(1 + r)) = 144
100(1 + 1r + (1 * r + r * r)) = 144
100(1 + 1r + (1r + r2)) = 144

Combine like terms: 1r + 1r = 2r
100(1 + 2r + r2) = 144
(1 * 100 + 2r * 100 + r2 * 100) = 144
(100 + 200r + 100r2) = 144

Solving
100 + 200r + 100r2 = 144

Solving for variable 'r'.

Reorder the terms:
100 + -144 + 200r + 100r2 = 144 + -144

Combine like terms: 100 + -144 = -44
-44 + 200r + 100r2 = 144 + -144

Combine like terms: 144 + -144 = 0
-44 + 200r + 100r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + 50r + 25r2) = 0

Factor a trinomial.
4((-11 + -5r)(1 + -5r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + -5r)' equal to zero and attempt to solve:

Simplifying
-11 + -5r = 0

Solving
-11 + -5r = 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 + -5r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -5r = 0 + 11
-5r = 0 + 11

Combine like terms: 0 + 11 = 11
-5r = 11

Divide each side by '-5'.
r = -2.2

Simplifying
r = -2.2
Subproblem 2
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

Solving
1 + -5r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5r = 0 + -1
-5r = 0 + -1

Combine like terms: 0 + -1 = -1
-5r = -1

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-2.2, 0.2}