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

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


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

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

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

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

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

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

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

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

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

Solving
81x2 = 81x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '81x'.
81x(-1 + x) = 0

Ignore the factor 81.

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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