(2x-3)x(5x+10)=0

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Solution for (2x-3)x(5x+10)=0 equation:


Simplifying
(2x + -3) * x(5x + 10) = 0

Reorder the terms:
(-3 + 2x) * x(5x + 10) = 0

Reorder the terms:
(-3 + 2x) * x(10 + 5x) = 0

Reorder the terms for easier multiplication:
x(-3 + 2x)(10 + 5x) = 0

Multiply (-3 + 2x) * (10 + 5x)
x(-3(10 + 5x) + 2x * (10 + 5x)) = 0
x((10 * -3 + 5x * -3) + 2x * (10 + 5x)) = 0
x((-30 + -15x) + 2x * (10 + 5x)) = 0
x(-30 + -15x + (10 * 2x + 5x * 2x)) = 0
x(-30 + -15x + (20x + 10x2)) = 0

Combine like terms: -15x + 20x = 5x
x(-30 + 5x + 10x2) = 0
(-30 * x + 5x * x + 10x2 * x) = 0
(-30x + 5x2 + 10x3) = 0

Solving
-30x + 5x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-6 + x + 2x2) = 0

Factor a trinomial.
5x((-2 + -1x)(3 + -2x)) = 0

Ignore the factor 5.

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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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, 1.5}

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