10X^2-24=30-12X

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Solution for 10X^2-24=30-12X equation: 


Simplifying
10X2 + -24 = 30 + -12X

Reorder the terms:
-24 + 10X2 = 30 + -12X

Solving
-24 + 10X2 = 30 + -12X

Solving for variable 'X'.

Reorder the terms:
-24 + -30 + 12X + 10X2 = 30 + -12X + -30 + 12X

Combine like terms: -24 + -30 = -54
-54 + 12X + 10X2 = 30 + -12X + -30 + 12X

Reorder the terms:
-54 + 12X + 10X2 = 30 + -30 + -12X + 12X

Combine like terms: 30 + -30 = 0
-54 + 12X + 10X2 = 0 + -12X + 12X
-54 + 12X + 10X2 = -12X + 12X

Combine like terms: -12X + 12X = 0
-54 + 12X + 10X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 6X + 5X2) = 0

Factor a trinomial.
2((-3 + -1X)(9 + -5X)) = 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 '(9 + -5X)' equal to zero and attempt to solve:

Simplifying
9 + -5X = 0

Solving
9 + -5X = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5X = 0 + -9
-5X = 0 + -9

Combine like terms: 0 + -9 = -9
-5X = -9

Divide each side by '-5'.
X = 1.8

Simplifying
X = 1.8
Solution
X = {-3, 1.8}

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