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

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


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

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

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

Combine like terms: 5x + -9x = -4x
3(-15 + -4x + 3x2) = 0
(-15 * 3 + -4x * 3 + 3x2 * 3) = 0
(-45 + -12x + 9x2) = 0

Solving
-45 + -12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -4x + 3x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {-1.666666667, 3}

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