3x(2x-5)(3x-2)=

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


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

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

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

Multiply (-5 + 2x) * (-2 + 3x)
3x(-5(-2 + 3x) + 2x * (-2 + 3x)) = 0
3x((-2 * -5 + 3x * -5) + 2x * (-2 + 3x)) = 0
3x((10 + -15x) + 2x * (-2 + 3x)) = 0
3x(10 + -15x + (-2 * 2x + 3x * 2x)) = 0
3x(10 + -15x + (-4x + 6x2)) = 0

Combine like terms: -15x + -4x = -19x
3x(10 + -19x + 6x2) = 0
(10 * 3x + -19x * 3x + 6x2 * 3x) = 0
(30x + -57x2 + 18x3) = 0

Solving
30x + -57x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(10 + -19x + 6x2) = 0

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

Ignore the factor 3.

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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Subproblem 3

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, 0.6666666667, 2.5}

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