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

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


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

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

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

Multiply (-5 + 4x) * (3 + x)
x(-5(3 + x) + 4x * (3 + x)) = 0
x((3 * -5 + x * -5) + 4x * (3 + x)) = 0
x((-15 + -5x) + 4x * (3 + x)) = 0
x(-15 + -5x + (3 * 4x + x * 4x)) = 0
x(-15 + -5x + (12x + 4x2)) = 0

Combine like terms: -5x + 12x = 7x
x(-15 + 7x + 4x2) = 0
(-15 * x + 7x * x + 4x2 * x) = 0
(-15x + 7x2 + 4x3) = 0

Solving
-15x + 7x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + 7x + 4x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0, -3, 1.25}

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