(15x+10)(15x-10)=225x-100

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Solution for (15x+10)(15x-10)=225x-100 equation: 


Simplifying
(15x + 10)(15x + -10) = 225x + -100

Reorder the terms:
(10 + 15x)(15x + -10) = 225x + -100

Reorder the terms:
(10 + 15x)(-10 + 15x) = 225x + -100

Multiply (10 + 15x) * (-10 + 15x)
(10(-10 + 15x) + 15x * (-10 + 15x)) = 225x + -100
((-10 * 10 + 15x * 10) + 15x * (-10 + 15x)) = 225x + -100
((-100 + 150x) + 15x * (-10 + 15x)) = 225x + -100
(-100 + 150x + (-10 * 15x + 15x * 15x)) = 225x + -100
(-100 + 150x + (-150x + 225x2)) = 225x + -100

Combine like terms: 150x + -150x = 0
(-100 + 0 + 225x2) = 225x + -100
(-100 + 225x2) = 225x + -100

Reorder the terms:
-100 + 225x2 = -100 + 225x

Add '100' to each side of the equation.
-100 + 100 + 225x2 = -100 + 100 + 225x

Combine like terms: -100 + 100 = 0
0 + 225x2 = -100 + 100 + 225x
225x2 = -100 + 100 + 225x

Combine like terms: -100 + 100 = 0
225x2 = 0 + 225x
225x2 = 225x

Solving
225x2 = 225x

Solving for variable 'x'.

Reorder the terms:
-225x + 225x2 = 225x + -225x

Combine like terms: 225x + -225x = 0
-225x + 225x2 = 0

Factor out the Greatest Common Factor (GCF), '225x'.
225x(-1 + x) = 0

Ignore the factor 225.

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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