(3x-2x^2)(5+4x)=0

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Solution for (3x-2x^2)(5+4x)=0 equation: 


Simplifying
(3x + -2x2)(5 + 4x) = 0

Multiply (3x + -2x2) * (5 + 4x)
(3x * (5 + 4x) + -2x2 * (5 + 4x)) = 0
((5 * 3x + 4x * 3x) + -2x2 * (5 + 4x)) = 0
((15x + 12x2) + -2x2 * (5 + 4x)) = 0
(15x + 12x2 + (5 * -2x2 + 4x * -2x2)) = 0
(15x + 12x2 + (-10x2 + -8x3)) = 0

Combine like terms: 12x2 + -10x2 = 2x2
(15x + 2x2 + -8x3) = 0

Solving
15x + 2x2 + -8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + 2x + -8x2) = 0

Factor a trinomial.
x((3 + -2x)(5 + 4x)) = 0


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 '(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

Subproblem 3
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
Solution
x = {0, 1.5, -1.25}

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