(3X+4)(2X-6)=6X^2-CX-24

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Solution for (3X+4)(2X-6)=6X^2-CX-24 equation: 


Simplifying
(3X + 4)(2X + -6) = 6X2 + -1CX + -24

Reorder the terms:
(4 + 3X)(2X + -6) = 6X2 + -1CX + -24

Reorder the terms:
(4 + 3X)(-6 + 2X) = 6X2 + -1CX + -24

Multiply (4 + 3X) * (-6 + 2X)
(4(-6 + 2X) + 3X * (-6 + 2X)) = 6X2 + -1CX + -24
((-6 * 4 + 2X * 4) + 3X * (-6 + 2X)) = 6X2 + -1CX + -24
((-24 + 8X) + 3X * (-6 + 2X)) = 6X2 + -1CX + -24
(-24 + 8X + (-6 * 3X + 2X * 3X)) = 6X2 + -1CX + -24
(-24 + 8X + (-18X + 6X2)) = 6X2 + -1CX + -24

Combine like terms: 8X + -18X = -10X
(-24 + -10X + 6X2) = 6X2 + -1CX + -24

Reorder the terms:
-24 + -10X + 6X2 = -24 + -1CX + 6X2

Add '24' to each side of the equation.
-24 + -10X + 24 + 6X2 = -24 + -1CX + 24 + 6X2

Reorder the terms:
-24 + 24 + -10X + 6X2 = -24 + -1CX + 24 + 6X2

Combine like terms: -24 + 24 = 0
0 + -10X + 6X2 = -24 + -1CX + 24 + 6X2
-10X + 6X2 = -24 + -1CX + 24 + 6X2

Reorder the terms:
-10X + 6X2 = -24 + 24 + -1CX + 6X2

Combine like terms: -24 + 24 = 0
-10X + 6X2 = 0 + -1CX + 6X2
-10X + 6X2 = -1CX + 6X2

Add '-6X2' to each side of the equation.
-10X + 6X2 + -6X2 = -1CX + 6X2 + -6X2

Combine like terms: 6X2 + -6X2 = 0
-10X + 0 = -1CX + 6X2 + -6X2
-10X = -1CX + 6X2 + -6X2

Combine like terms: 6X2 + -6X2 = 0
-10X = -1CX + 0
-10X = -1CX

Solving
-10X = -1CX

Solving for variable 'X'.

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

Add 'CX' to each side of the equation.
CX + -10X = -1CX + CX

Combine like terms: -1CX + CX = 0
CX + -10X = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(C + -10) = 0


Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0

Subproblem 2
Set the factor '(C + -10)' equal to zero and attempt to solve:

Simplifying
C + -10 = 0

Reorder the terms:
-10 + C = 0

Solving
-10 + C = 0

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

Add '10' to each side of the equation.
-10 + 10 + C = 0 + 10

Combine like terms: -10 + 10 = 0
0 + C = 0 + 10
C = 0 + 10

Combine like terms: 0 + 10 = 10
C = 10

Add '-1C' to each side of the equation.
C + -1C = 10 + -1C

Combine like terms: C + -1C = 0
0 = 10 + -1C

Simplifying
0 = 10 + -1C

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}

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