4x(3x+2)(2x+5)=

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


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

Reorder the terms:
4x(2 + 3x)(2x + 5) = 0

Reorder the terms:
4x(2 + 3x)(5 + 2x) = 0

Multiply (2 + 3x) * (5 + 2x)
4x(2(5 + 2x) + 3x * (5 + 2x)) = 0
4x((5 * 2 + 2x * 2) + 3x * (5 + 2x)) = 0
4x((10 + 4x) + 3x * (5 + 2x)) = 0
4x(10 + 4x + (5 * 3x + 2x * 3x)) = 0
4x(10 + 4x + (15x + 6x2)) = 0

Combine like terms: 4x + 15x = 19x
4x(10 + 19x + 6x2) = 0
(10 * 4x + 19x * 4x + 6x2 * 4x) = 0
(40x + 76x2 + 24x3) = 0

Solving
40x + 76x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(10 + 19x + 6x2) = 0

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

Ignore the factor 4.

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 '(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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -2.5, -0.6666666667}

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