(10x+9)(10x-9)=100x-81

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Solution for (10x+9)(10x-9)=100x-81 equation: 


Simplifying
(10x + 9)(10x + -9) = 100x + -81

Reorder the terms:
(9 + 10x)(10x + -9) = 100x + -81

Reorder the terms:
(9 + 10x)(-9 + 10x) = 100x + -81

Multiply (9 + 10x) * (-9 + 10x)
(9(-9 + 10x) + 10x * (-9 + 10x)) = 100x + -81
((-9 * 9 + 10x * 9) + 10x * (-9 + 10x)) = 100x + -81
((-81 + 90x) + 10x * (-9 + 10x)) = 100x + -81
(-81 + 90x + (-9 * 10x + 10x * 10x)) = 100x + -81
(-81 + 90x + (-90x + 100x2)) = 100x + -81

Combine like terms: 90x + -90x = 0
(-81 + 0 + 100x2) = 100x + -81
(-81 + 100x2) = 100x + -81

Reorder the terms:
-81 + 100x2 = -81 + 100x

Add '81' to each side of the equation.
-81 + 81 + 100x2 = -81 + 81 + 100x

Combine like terms: -81 + 81 = 0
0 + 100x2 = -81 + 81 + 100x
100x2 = -81 + 81 + 100x

Combine like terms: -81 + 81 = 0
100x2 = 0 + 100x
100x2 = 100x

Solving
100x2 = 100x

Solving for variable 'x'.

Reorder the terms:
-100x + 100x2 = 100x + -100x

Combine like terms: 100x + -100x = 0
-100x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100x'.
100x(-1 + x) = 0

Ignore the factor 100.

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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