4r^2=25r+21

Solution for 4r^2=25r+21 equation:

Simplifying
4r2 = 25r + 21

Reorder the terms:
4r2 = 21 + 25r

Solving
4r2 = 21 + 25r

Solving for variable 'r'.

Reorder the terms:
-21 + -25r + 4r2 = 21 + 25r + -21 + -25r

Reorder the terms:
-21 + -25r + 4r2 = 21 + -21 + 25r + -25r

Combine like terms: 21 + -21 = 0
-21 + -25r + 4r2 = 0 + 25r + -25r
-21 + -25r + 4r2 = 25r + -25r

Combine like terms: 25r + -25r = 0
-21 + -25r + 4r2 = 0

Factor a trinomial.
(-3 + -4r)(7 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -4r)' equal to zero and attempt to solve:

Simplifying
-3 + -4r = 0

Solving
-3 + -4r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4r = 0 + 3
-4r = 0 + 3

Combine like terms: 0 + 3 = 3
-4r = 3

Divide each side by '-4'.
r = -0.75

Simplifying
r = -0.75
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-0.75, 7}