(r-7)(2r+9)=0

Solution for (r-7)(2r+9)=0 equation:

Simplifying
(r + -7)(2r + 9) = 0

Reorder the terms:
(-7 + r)(2r + 9) = 0

Reorder the terms:
(-7 + r)(9 + 2r) = 0

Multiply (-7 + r) * (9 + 2r)
(-7(9 + 2r) + r(9 + 2r)) = 0
((9 * -7 + 2r * -7) + r(9 + 2r)) = 0
((-63 + -14r) + r(9 + 2r)) = 0
(-63 + -14r + (9 * r + 2r * r)) = 0
(-63 + -14r + (9r + 2r2)) = 0

Combine like terms: -14r + 9r = -5r
(-63 + -5r + 2r2) = 0

Solving
-63 + -5r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -2r)(7 + -1r) = 0

Subproblem 1
Set the factor '(-9 + -2r)' equal to zero and attempt to solve:

Simplifying
-9 + -2r = 0

Solving
-9 + -2r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2r = 0 + 9
-2r = 0 + 9

Combine like terms: 0 + 9 = 9
-2r = 9

Divide each side by '-2'.
r = -4.5

Simplifying
r = -4.5
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 = {-4.5, 7}