6X^2+9X-18=4X^2+5X-12

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Solution for 6X^2+9X-18=4X^2+5X-12 equation: 


Simplifying
6X2 + 9X + -18 = 4X2 + 5X + -12

Reorder the terms:
-18 + 9X + 6X2 = 4X2 + 5X + -12

Reorder the terms:
-18 + 9X + 6X2 = -12 + 5X + 4X2

Solving
-18 + 9X + 6X2 = -12 + 5X + 4X2

Solving for variable 'X'.

Reorder the terms:
-18 + 12 + 9X + -5X + 6X2 + -4X2 = -12 + 5X + 4X2 + 12 + -5X + -4X2

Combine like terms: -18 + 12 = -6
-6 + 9X + -5X + 6X2 + -4X2 = -12 + 5X + 4X2 + 12 + -5X + -4X2

Combine like terms: 9X + -5X = 4X
-6 + 4X + 6X2 + -4X2 = -12 + 5X + 4X2 + 12 + -5X + -4X2

Combine like terms: 6X2 + -4X2 = 2X2
-6 + 4X + 2X2 = -12 + 5X + 4X2 + 12 + -5X + -4X2

Reorder the terms:
-6 + 4X + 2X2 = -12 + 12 + 5X + -5X + 4X2 + -4X2

Combine like terms: -12 + 12 = 0
-6 + 4X + 2X2 = 0 + 5X + -5X + 4X2 + -4X2
-6 + 4X + 2X2 = 5X + -5X + 4X2 + -4X2

Combine like terms: 5X + -5X = 0
-6 + 4X + 2X2 = 0 + 4X2 + -4X2
-6 + 4X + 2X2 = 4X2 + -4X2

Combine like terms: 4X2 + -4X2 = 0
-6 + 4X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2X + X2) = 0

Factor a trinomial.
2((-3 + -1X)(1 + -1X)) = 0

Ignore the factor 2.

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 '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
Solution
X = {-3, 1}

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