(3x+6)*(x-5)=0

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Solution for (3x+6)*(x-5)=0 equation:


Simplifying
(3x + 6)(x + -5) = 0

Reorder the terms:
(6 + 3x)(x + -5) = 0

Reorder the terms:
(6 + 3x)(-5 + x) = 0

Multiply (6 + 3x) * (-5 + x)
(6(-5 + x) + 3x * (-5 + x)) = 0
((-5 * 6 + x * 6) + 3x * (-5 + x)) = 0
((-30 + 6x) + 3x * (-5 + x)) = 0
(-30 + 6x + (-5 * 3x + x * 3x)) = 0
(-30 + 6x + (-15x + 3x2)) = 0

Combine like terms: 6x + -15x = -9x
(-30 + -9x + 3x2) = 0

Solving
-30 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(5 + -1x)) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-2, 5}

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