(3x-12)(10+2x)=0

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Solution for (3x-12)(10+2x)=0 equation: 


Simplifying
(3x + -12)(10 + 2x) = 0

Reorder the terms:
(-12 + 3x)(10 + 2x) = 0

Multiply (-12 + 3x) * (10 + 2x)
(-12(10 + 2x) + 3x * (10 + 2x)) = 0
((10 * -12 + 2x * -12) + 3x * (10 + 2x)) = 0
((-120 + -24x) + 3x * (10 + 2x)) = 0
(-120 + -24x + (10 * 3x + 2x * 3x)) = 0
(-120 + -24x + (30x + 6x2)) = 0

Combine like terms: -24x + 30x = 6x
(-120 + 6x + 6x2) = 0

Solving
-120 + 6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + x + x2) = 0

Factor a trinomial.
6((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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