t^2-3t-12=3t^2+8

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Solution for t^2-3t-12=3t^2+8 equation: 


Simplifying
t2 + -3t + -12 = 3t2 + 8

Reorder the terms:
-12 + -3t + t2 = 3t2 + 8

Reorder the terms:
-12 + -3t + t2 = 8 + 3t2

Solving
-12 + -3t + t2 = 8 + 3t2

Solving for variable 't'.

Reorder the terms:
-12 + -8 + -3t + t2 + -3t2 = 8 + 3t2 + -8 + -3t2

Combine like terms: -12 + -8 = -20
-20 + -3t + t2 + -3t2 = 8 + 3t2 + -8 + -3t2

Combine like terms: t2 + -3t2 = -2t2
-20 + -3t + -2t2 = 8 + 3t2 + -8 + -3t2

Reorder the terms:
-20 + -3t + -2t2 = 8 + -8 + 3t2 + -3t2

Combine like terms: 8 + -8 = 0
-20 + -3t + -2t2 = 0 + 3t2 + -3t2
-20 + -3t + -2t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-20 + -3t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 3t + 2t2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(20 + 3t + 2t2)' equal to zero and attempt to solve:

Simplifying
20 + 3t + 2t2 = 0

Solving
20 + 3t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
10 + 1.5t + t2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 1.5t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 1.5t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 1.5t + t2 = 0 + -10
1.5t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
1.5t + t2 = -10

The t term is 1.5t.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5t + 0.5625 + t2 = -10 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = -10 + 0.5625

Combine like terms: -10 + 0.5625 = -9.4375
0.5625 + 1.5t + t2 = -9.4375

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = -9.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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