(2x+3)(6x^2+x)=0

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Solution for (2x+3)(6x^2+x)=0 equation:


Simplifying
(2x + 3)(6x2 + x) = 0

Reorder the terms:
(3 + 2x)(6x2 + x) = 0

Reorder the terms:
(3 + 2x)(x + 6x2) = 0

Multiply (3 + 2x) * (x + 6x2)
(3(x + 6x2) + 2x * (x + 6x2)) = 0
((x * 3 + 6x2 * 3) + 2x * (x + 6x2)) = 0
((3x + 18x2) + 2x * (x + 6x2)) = 0
(3x + 18x2 + (x * 2x + 6x2 * 2x)) = 0
(3x + 18x2 + (2x2 + 12x3)) = 0

Combine like terms: 18x2 + 2x2 = 20x2
(3x + 20x2 + 12x3) = 0

Solving
3x + 20x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + 20x + 12x2) = 0

Factor a trinomial.
x((3 + 2x)(1 + 6x)) = 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 '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667

Solution

x = {0, -1.5, -0.1666666667}

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