r^2-19r=-7r+64

Solution for r^2-19r=-7r+64 equation:

Simplifying
r2 + -19r = -7r + 64

Reorder the terms:
-19r + r2 = -7r + 64

Reorder the terms:
-19r + r2 = 64 + -7r

Solving
-19r + r2 = 64 + -7r

Solving for variable 'r'.

Reorder the terms:
-64 + -19r + 7r + r2 = 64 + -7r + -64 + 7r

Combine like terms: -19r + 7r = -12r
-64 + -12r + r2 = 64 + -7r + -64 + 7r

Reorder the terms:
-64 + -12r + r2 = 64 + -64 + -7r + 7r

Combine like terms: 64 + -64 = 0
-64 + -12r + r2 = 0 + -7r + 7r
-64 + -12r + r2 = -7r + 7r

Combine like terms: -7r + 7r = 0
-64 + -12r + r2 = 0

Factor a trinomial.
(-4 + -1r)(16 + -1r) = 0

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

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(16 + -1r)' equal to zero and attempt to solve:

Simplifying
16 + -1r = 0

Solving
16 + -1r = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1r = 0 + -16
-1r = 0 + -16

Combine like terms: 0 + -16 = -16
-1r = -16

Divide each side by '-1'.
r = 16

Simplifying
r = 16
Solution
r = {-4, 16}