(4X+12)(5X-3)=0

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Solution for (4X+12)(5X-3)=0 equation: 


Simplifying
(4X + 12)(5X + -3) = 0

Reorder the terms:
(12 + 4X)(5X + -3) = 0

Reorder the terms:
(12 + 4X)(-3 + 5X) = 0

Multiply (12 + 4X) * (-3 + 5X)
(12(-3 + 5X) + 4X * (-3 + 5X)) = 0
((-3 * 12 + 5X * 12) + 4X * (-3 + 5X)) = 0
((-36 + 60X) + 4X * (-3 + 5X)) = 0
(-36 + 60X + (-3 * 4X + 5X * 4X)) = 0
(-36 + 60X + (-12X + 20X2)) = 0

Combine like terms: 60X + -12X = 48X
(-36 + 48X + 20X2) = 0

Solving
-36 + 48X + 20X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 12X + 5X2) = 0

Factor a trinomial.
4((-3 + -1X)(3 + -5X)) = 0

Ignore the factor 4.

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

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 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 + -1X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X = 0 + 3
-1X = 0 + 3

Combine like terms: 0 + 3 = 3
-1X = 3

Divide each side by '-1'.
X = -3

Simplifying
X = -3

Subproblem 2
Set the factor '(3 + -5X)' equal to zero and attempt to solve:

Simplifying
3 + -5X = 0

Solving
3 + -5X = 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 + -5X = 0 + -3

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

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

Divide each side by '-5'.
X = 0.6

Simplifying
X = 0.6
Solution
X = {-3, 0.6}

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