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

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


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

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

Multiply (6x + 4x2) * (5x + -2x2)
(6x * (5x + -2x2) + 4x2 * (5x + -2x2)) = 0
((5x * 6x + -2x2 * 6x) + 4x2 * (5x + -2x2)) = 0
((30x2 + -12x3) + 4x2 * (5x + -2x2)) = 0
(30x2 + -12x3 + (5x * 4x2 + -2x2 * 4x2)) = 0
(30x2 + -12x3 + (20x3 + -8x4)) = 0

Combine like terms: -12x3 + 20x3 = 8x3
(30x2 + 8x3 + -8x4) = 0

Solving
30x2 + 8x3 + -8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(15 + 4x + -4x2) = 0

Factor a trinomial.
2x2((5 + -2x)(3 + 2x)) = 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 + -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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, 2.5, -1.5}

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