9t^2-24t+18=-3t^2+18t-12

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Solution for 9t^2-24t+18=-3t^2+18t-12 equation: 


Simplifying
9t2 + -24t + 18 = -3t2 + 18t + -12

Reorder the terms:
18 + -24t + 9t2 = -3t2 + 18t + -12

Reorder the terms:
18 + -24t + 9t2 = -12 + 18t + -3t2

Solving
18 + -24t + 9t2 = -12 + 18t + -3t2

Solving for variable 't'.

Reorder the terms:
18 + 12 + -24t + -18t + 9t2 + 3t2 = -12 + 18t + -3t2 + 12 + -18t + 3t2

Combine like terms: 18 + 12 = 30
30 + -24t + -18t + 9t2 + 3t2 = -12 + 18t + -3t2 + 12 + -18t + 3t2

Combine like terms: -24t + -18t = -42t
30 + -42t + 9t2 + 3t2 = -12 + 18t + -3t2 + 12 + -18t + 3t2

Combine like terms: 9t2 + 3t2 = 12t2
30 + -42t + 12t2 = -12 + 18t + -3t2 + 12 + -18t + 3t2

Reorder the terms:
30 + -42t + 12t2 = -12 + 12 + 18t + -18t + -3t2 + 3t2

Combine like terms: -12 + 12 = 0
30 + -42t + 12t2 = 0 + 18t + -18t + -3t2 + 3t2
30 + -42t + 12t2 = 18t + -18t + -3t2 + 3t2

Combine like terms: 18t + -18t = 0
30 + -42t + 12t2 = 0 + -3t2 + 3t2
30 + -42t + 12t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
30 + -42t + 12t2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -7t + 2t2) = 0

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

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1

Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {1, 2.5}

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