3(4x-3)(2x+5)=0

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Solution for 3(4x-3)(2x+5)=0 equation: 


Simplifying
3(4x + -3)(2x + 5) = 0

Reorder the terms:
3(-3 + 4x)(2x + 5) = 0

Reorder the terms:
3(-3 + 4x)(5 + 2x) = 0

Multiply (-3 + 4x) * (5 + 2x)
3(-3(5 + 2x) + 4x * (5 + 2x)) = 0
3((5 * -3 + 2x * -3) + 4x * (5 + 2x)) = 0
3((-15 + -6x) + 4x * (5 + 2x)) = 0
3(-15 + -6x + (5 * 4x + 2x * 4x)) = 0
3(-15 + -6x + (20x + 8x2)) = 0

Combine like terms: -6x + 20x = 14x
3(-15 + 14x + 8x2) = 0
(-15 * 3 + 14x * 3 + 8x2 * 3) = 0
(-45 + 42x + 24x2) = 0

Solving
-45 + 42x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 14x + 8x2) = 0

Factor a trinomial.
3((-5 + -2x)(3 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-2.5, 0.75}

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