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

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


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

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

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

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

Combine like terms: -20x + 6x = -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((-3 + -4x)(5 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.75, 2.5}

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