(15x+12)(15x-12)=255x-144

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Solution for (15x+12)(15x-12)=255x-144 equation: 


Simplifying
(15x + 12)(15x + -12) = 255x + -144

Reorder the terms:
(12 + 15x)(15x + -12) = 255x + -144

Reorder the terms:
(12 + 15x)(-12 + 15x) = 255x + -144

Multiply (12 + 15x) * (-12 + 15x)
(12(-12 + 15x) + 15x * (-12 + 15x)) = 255x + -144
((-12 * 12 + 15x * 12) + 15x * (-12 + 15x)) = 255x + -144
((-144 + 180x) + 15x * (-12 + 15x)) = 255x + -144
(-144 + 180x + (-12 * 15x + 15x * 15x)) = 255x + -144
(-144 + 180x + (-180x + 225x2)) = 255x + -144

Combine like terms: 180x + -180x = 0
(-144 + 0 + 225x2) = 255x + -144
(-144 + 225x2) = 255x + -144

Reorder the terms:
-144 + 225x2 = -144 + 255x

Add '144' to each side of the equation.
-144 + 144 + 225x2 = -144 + 144 + 255x

Combine like terms: -144 + 144 = 0
0 + 225x2 = -144 + 144 + 255x
225x2 = -144 + 144 + 255x

Combine like terms: -144 + 144 = 0
225x2 = 0 + 255x
225x2 = 255x

Solving
225x2 = 255x

Solving for variable 'x'.

Reorder the terms:
-255x + 225x2 = 255x + -255x

Combine like terms: 255x + -255x = 0
-255x + 225x2 = 0

Factor out the Greatest Common Factor (GCF), '15x'.
15x(-17 + 15x) = 0

Ignore the factor 15.

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 '(-17 + 15x)' equal to zero and attempt to solve:

Simplifying
-17 + 15x = 0

Solving
-17 + 15x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 15x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 15x = 0 + 17
15x = 0 + 17

Combine like terms: 0 + 17 = 17
15x = 17

Divide each side by '15'.
x = 1.133333333

Simplifying
x = 1.133333333
Solution
x = {0, 1.133333333}

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