3(3x-4)(x+5)=0

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Solution for 3(3x-4)(x+5)=0 equation: 


Simplifying
3(3x + -4)(x + 5) = 0

Reorder the terms:
3(-4 + 3x)(x + 5) = 0

Reorder the terms:
3(-4 + 3x)(5 + x) = 0

Multiply (-4 + 3x) * (5 + x)
3(-4(5 + x) + 3x * (5 + x)) = 0
3((5 * -4 + x * -4) + 3x * (5 + x)) = 0
3((-20 + -4x) + 3x * (5 + x)) = 0
3(-20 + -4x + (5 * 3x + x * 3x)) = 0
3(-20 + -4x + (15x + 3x2)) = 0

Combine like terms: -4x + 15x = 11x
3(-20 + 11x + 3x2) = 0
(-20 * 3 + 11x * 3 + 3x2 * 3) = 0
(-60 + 33x + 9x2) = 0

Solving
-60 + 33x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + 11x + 3x2) = 0

Factor a trinomial.
3((-5 + -1x)(4 + -3x)) = 0

Ignore the factor 3.

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

Simplifying
-5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-5, 1.333333333}

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