(3x-9)(5x-15)=0

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Solution for (3x-9)(5x-15)=0 equation: 


Simplifying
(3x + -9)(5x + -15) = 0

Reorder the terms:
(-9 + 3x)(5x + -15) = 0

Reorder the terms:
(-9 + 3x)(-15 + 5x) = 0

Multiply (-9 + 3x) * (-15 + 5x)
(-9(-15 + 5x) + 3x * (-15 + 5x)) = 0
((-15 * -9 + 5x * -9) + 3x * (-15 + 5x)) = 0
((135 + -45x) + 3x * (-15 + 5x)) = 0
(135 + -45x + (-15 * 3x + 5x * 3x)) = 0
(135 + -45x + (-45x + 15x2)) = 0

Combine like terms: -45x + -45x = -90x
(135 + -90x + 15x2) = 0

Solving
135 + -90x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(9 + -6x + x2) = 0

Factor a trinomial.
15((3 + -1x)(3 + -1x)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}

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