(x+9)(x-9)=x^2+rx+t

Solution for (x+9)(x-9)=x^2+rx+t equation:

Simplifying
(x + 9)(x + -9) = x2 + rx + t

Reorder the terms:
(9 + x)(x + -9) = x2 + rx + t

Reorder the terms:
(9 + x)(-9 + x) = x2 + rx + t

Multiply (9 + x) * (-9 + x)
(9(-9 + x) + x(-9 + x)) = x2 + rx + t
((-9 * 9 + x * 9) + x(-9 + x)) = x2 + rx + t
((-81 + 9x) + x(-9 + x)) = x2 + rx + t
(-81 + 9x + (-9 * x + x * x)) = x2 + rx + t
(-81 + 9x + (-9x + x2)) = x2 + rx + t

Combine like terms: 9x + -9x = 0
(-81 + 0 + x2) = x2 + rx + t
(-81 + x2) = x2 + rx + t

Reorder the terms:
-81 + x2 = rx + t + x2

Add '-1x2' to each side of the equation.
-81 + x2 + -1x2 = rx + t + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-81 + 0 = rx + t + x2 + -1x2
-81 = rx + t + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-81 = rx + t + 0
-81 = rx + t

Solving
-81 = rx + t

Solving for variable 'r'.

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

Add '-1rx' to each side of the equation.
-81 + -1rx = rx + -1rx + t

Combine like terms: rx + -1rx = 0
-81 + -1rx = 0 + t
-81 + -1rx = t

Add '81' to each side of the equation.
-81 + 81 + -1rx = 81 + t

Combine like terms: -81 + 81 = 0
0 + -1rx = 81 + t
-1rx = 81 + t

Divide each side by '-1x'.
r = -81x-1 + -1tx-1

Simplifying
r = -81x-1 + -1tx-1

Reorder the terms:
r = -1tx-1 + -81x-1