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

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


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

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

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

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

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

Combine like terms: 8x + 15x = 23x
x(-20 + 23x + -6x2) = 0
(-20 * x + 23x * x + -6x2 * x) = 0
(-20x + 23x2 + -6x3) = 0

Solving
-20x + 23x2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20 + 23x + -6x2) = 0

Factor a trinomial.
x((-5 + 2x)(4 + -3x)) = 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 '(-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 3
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 = {0, 2.5, 1.333333333}

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