(2x^2-4x)(6x^2-5x)=

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Solution for (2x^2-4x)(6x^2-5x)= equation: 


Simplifying
(2x2 + -4x)(6x2 + -5x) = 0

Reorder the terms:
(-4x + 2x2)(6x2 + -5x) = 0

Reorder the terms:
(-4x + 2x2)(-5x + 6x2) = 0

Multiply (-4x + 2x2) * (-5x + 6x2)
(-4x * (-5x + 6x2) + 2x2 * (-5x + 6x2)) = 0
((-5x * -4x + 6x2 * -4x) + 2x2 * (-5x + 6x2)) = 0
((20x2 + -24x3) + 2x2 * (-5x + 6x2)) = 0
(20x2 + -24x3 + (-5x * 2x2 + 6x2 * 2x2)) = 0
(20x2 + -24x3 + (-10x3 + 12x4)) = 0

Combine like terms: -24x3 + -10x3 = -34x3
(20x2 + -34x3 + 12x4) = 0

Solving
20x2 + -34x3 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(10 + -17x + 6x2) = 0

Factor a trinomial.
2x2((5 + -6x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 0.8333333333, 2}

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