(2x^2+x)(x-6)=0

Solution for (2x^2+x)(x-6)=0 equation:

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

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

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

Multiply (x + 2x2) * (-6 + x)
(x(-6 + x) + 2x2 * (-6 + x)) = 0
((-6 * x + x * x) + 2x2 * (-6 + x)) = 0
((-6x + x2) + 2x2 * (-6 + x)) = 0
(-6x + x2 + (-6 * 2x2 + x * 2x2)) = 0
(-6x + x2 + (-12x2 + 2x3)) = 0

Combine like terms: x2 + -12x2 = -11x2
(-6x + -11x2 + 2x3) = 0

Solving
-6x + -11x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -11x + 2x2) = 0

Factor a trinomial.
x((-1 + -2x)(6 + -1x)) = 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 '(-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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -0.5, 6}