3(3x+5)(-5x+1)=0

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Solution for 3(3x+5)(-5x+1)=0 equation: 


Simplifying
3(3x + 5)(-5x + 1) = 0

Reorder the terms:
3(5 + 3x)(-5x + 1) = 0

Reorder the terms:
3(5 + 3x)(1 + -5x) = 0

Multiply (5 + 3x) * (1 + -5x)
3(5(1 + -5x) + 3x * (1 + -5x)) = 0
3((1 * 5 + -5x * 5) + 3x * (1 + -5x)) = 0
3((5 + -25x) + 3x * (1 + -5x)) = 0
3(5 + -25x + (1 * 3x + -5x * 3x)) = 0
3(5 + -25x + (3x + -15x2)) = 0

Combine like terms: -25x + 3x = -22x
3(5 + -22x + -15x2) = 0
(5 * 3 + -22x * 3 + -15x2 * 3) = 0
(15 + -66x + -45x2) = 0

Solving
15 + -66x + -45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -22x + -15x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0.2, -1.666666667}

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