(7x-3)(5x-15)=0

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Solution for (7x-3)(5x-15)=0 equation: 


Simplifying
(7x + -3)(5x + -15) = 0

Reorder the terms:
(-3 + 7x)(5x + -15) = 0

Reorder the terms:
(-3 + 7x)(-15 + 5x) = 0

Multiply (-3 + 7x) * (-15 + 5x)
(-3(-15 + 5x) + 7x * (-15 + 5x)) = 0
((-15 * -3 + 5x * -3) + 7x * (-15 + 5x)) = 0
((45 + -15x) + 7x * (-15 + 5x)) = 0
(45 + -15x + (-15 * 7x + 5x * 7x)) = 0
(45 + -15x + (-105x + 35x2)) = 0

Combine like terms: -15x + -105x = -120x
(45 + -120x + 35x2) = 0

Solving
45 + -120x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(9 + -24x + 7x2) = 0

Factor a trinomial.
5((3 + -7x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286

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 = {0.4285714286, 3}

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