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

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


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

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

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

Multiply (2x + 4x2) * (-4 + 5x)
(2x * (-4 + 5x) + 4x2 * (-4 + 5x)) = 0
((-4 * 2x + 5x * 2x) + 4x2 * (-4 + 5x)) = 0
((-8x + 10x2) + 4x2 * (-4 + 5x)) = 0
(-8x + 10x2 + (-4 * 4x2 + 5x * 4x2)) = 0
(-8x + 10x2 + (-16x2 + 20x3)) = 0

Combine like terms: 10x2 + -16x2 = -6x2
(-8x + -6x2 + 20x3) = 0

Solving
-8x + -6x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + -3x + 10x2) = 0

Factor a trinomial.
2x((-1 + -2x)(4 + -5x)) = 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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
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
Solution
x = {0, -0.5, 0.8}

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