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

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


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

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

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

Multiply (-3 + x) * (4 + 5x)
2x(-3(4 + 5x) + x(4 + 5x)) = 0
2x((4 * -3 + 5x * -3) + x(4 + 5x)) = 0
2x((-12 + -15x) + x(4 + 5x)) = 0
2x(-12 + -15x + (4 * x + 5x * x)) = 0
2x(-12 + -15x + (4x + 5x2)) = 0

Combine like terms: -15x + 4x = -11x
2x(-12 + -11x + 5x2) = 0
(-12 * 2x + -11x * 2x + 5x2 * 2x) = 0
(-24x + -22x2 + 10x3) = 0

Solving
-24x + -22x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-12 + -11x + 5x2) = 0

Factor a trinomial.
2x((-4 + -5x)(3 + -1x)) = 0

Ignore the factor 2.

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 '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

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

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

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

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 3
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 = {0, -0.8, 3}

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