(4x-5)(2x^3-7x^2)=

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Solution for (4x-5)(2x^3-7x^2)= equation: 


Simplifying
(4x + -5)(2x3 + -7x2) = 0

Reorder the terms:
(-5 + 4x)(2x3 + -7x2) = 0

Reorder the terms:
(-5 + 4x)(-7x2 + 2x3) = 0

Multiply (-5 + 4x) * (-7x2 + 2x3)
(-5(-7x2 + 2x3) + 4x * (-7x2 + 2x3)) = 0
((-7x2 * -5 + 2x3 * -5) + 4x * (-7x2 + 2x3)) = 0
((35x2 + -10x3) + 4x * (-7x2 + 2x3)) = 0
(35x2 + -10x3 + (-7x2 * 4x + 2x3 * 4x)) = 0
(35x2 + -10x3 + (-28x3 + 8x4)) = 0

Combine like terms: -10x3 + -28x3 = -38x3
(35x2 + -38x3 + 8x4) = 0

Solving
35x2 + -38x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(35 + -38x + 8x2) = 0

Factor a trinomial.
x2((5 + -4x)(7 + -2x)) = 0


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 + -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

Subproblem 3
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 1.25, 3.5}

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