(x+9)(x-9)=3(x-27)

Solution for (x+9)(x-9)=3(x-27) equation:

Simplifying
(x + 9)(x + -9) = 3(x + -27)

Reorder the terms:
(9 + x)(x + -9) = 3(x + -27)

Reorder the terms:
(9 + x)(-9 + x) = 3(x + -27)

Multiply (9 + x) * (-9 + x)
(9(-9 + x) + x(-9 + x)) = 3(x + -27)
((-9 * 9 + x * 9) + x(-9 + x)) = 3(x + -27)
((-81 + 9x) + x(-9 + x)) = 3(x + -27)
(-81 + 9x + (-9 * x + x * x)) = 3(x + -27)
(-81 + 9x + (-9x + x2)) = 3(x + -27)

Combine like terms: 9x + -9x = 0
(-81 + 0 + x2) = 3(x + -27)
(-81 + x2) = 3(x + -27)

Reorder the terms:
-81 + x2 = 3(-27 + x)
-81 + x2 = (-27 * 3 + x * 3)
-81 + x2 = (-81 + 3x)

Add '81' to each side of the equation.
-81 + 81 + x2 = -81 + 81 + 3x

Combine like terms: -81 + 81 = 0
0 + x2 = -81 + 81 + 3x
x2 = -81 + 81 + 3x

Combine like terms: -81 + 81 = 0
x2 = 0 + 3x
x2 = 3x

Solving
x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-3x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, 3}