(5x+9)(5x-9)=25x-81

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Solution for (5x+9)(5x-9)=25x-81 equation: 


Simplifying
(5x + 9)(5x + -9) = 25x + -81

Reorder the terms:
(9 + 5x)(5x + -9) = 25x + -81

Reorder the terms:
(9 + 5x)(-9 + 5x) = 25x + -81

Multiply (9 + 5x) * (-9 + 5x)
(9(-9 + 5x) + 5x * (-9 + 5x)) = 25x + -81
((-9 * 9 + 5x * 9) + 5x * (-9 + 5x)) = 25x + -81
((-81 + 45x) + 5x * (-9 + 5x)) = 25x + -81
(-81 + 45x + (-9 * 5x + 5x * 5x)) = 25x + -81
(-81 + 45x + (-45x + 25x2)) = 25x + -81

Combine like terms: 45x + -45x = 0
(-81 + 0 + 25x2) = 25x + -81
(-81 + 25x2) = 25x + -81

Reorder the terms:
-81 + 25x2 = -81 + 25x

Add '81' to each side of the equation.
-81 + 81 + 25x2 = -81 + 81 + 25x

Combine like terms: -81 + 81 = 0
0 + 25x2 = -81 + 81 + 25x
25x2 = -81 + 81 + 25x

Combine like terms: -81 + 81 = 0
25x2 = 0 + 25x
25x2 = 25x

Solving
25x2 = 25x

Solving for variable 'x'.

Reorder the terms:
-25x + 25x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
-25x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25x'.
25x(-1 + x) = 0

Ignore the factor 25.

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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}

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