(x+2)*(6x-3)=0

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


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

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

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

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

Combine like terms: 12x + -3x = 9x
(-6 + 9x + 6x2) = 0

Solving
-6 + 9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

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 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

Solution

x = {-2, 0.5}

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