(3x+5)(2x-12)=0

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Solution for (3x+5)(2x-12)=0 equation: 


Simplifying
(3x + 5)(2x + -12) = 0

Reorder the terms:
(5 + 3x)(2x + -12) = 0

Reorder the terms:
(5 + 3x)(-12 + 2x) = 0

Multiply (5 + 3x) * (-12 + 2x)
(5(-12 + 2x) + 3x * (-12 + 2x)) = 0
((-12 * 5 + 2x * 5) + 3x * (-12 + 2x)) = 0
((-60 + 10x) + 3x * (-12 + 2x)) = 0
(-60 + 10x + (-12 * 3x + 2x * 3x)) = 0
(-60 + 10x + (-36x + 6x2)) = 0

Combine like terms: 10x + -36x = -26x
(-60 + -26x + 6x2) = 0

Solving
-60 + -26x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -13x + 3x2) = 0

Factor a trinomial.
2((-5 + -3x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
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 = {-1.666666667, 6}

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