(5-t^2)+6(t^2-8)-(t^2+12)=

Solution for (5-t^2)+6(t^2-8)-(t^2+12)= equation:

Simplifying
(5 + -1t2) + 6(t2 + -8) + -1(t2 + 12) = 0

Remove parenthesis around (5 + -1t2)
5 + -1t2 + 6(t2 + -8) + -1(t2 + 12) = 0

Reorder the terms:
5 + -1t2 + 6(-8 + t2) + -1(t2 + 12) = 0
5 + -1t2 + (-8 * 6 + t2 * 6) + -1(t2 + 12) = 0
5 + -1t2 + (-48 + 6t2) + -1(t2 + 12) = 0

Reorder the terms:
5 + -1t2 + -48 + 6t2 + -1(12 + t2) = 0
5 + -1t2 + -48 + 6t2 + (12 * -1 + t2 * -1) = 0
5 + -1t2 + -48 + 6t2 + (-12 + -1t2) = 0

Reorder the terms:
5 + -48 + -12 + -1t2 + 6t2 + -1t2 = 0

Combine like terms: 5 + -48 = -43
-43 + -12 + -1t2 + 6t2 + -1t2 = 0

Combine like terms: -43 + -12 = -55
-55 + -1t2 + 6t2 + -1t2 = 0

Combine like terms: -1t2 + 6t2 = 5t2
-55 + 5t2 + -1t2 = 0

Combine like terms: 5t2 + -1t2 = 4t2
-55 + 4t2 = 0

Solving
-55 + 4t2 = 0

Solving for variable 't'.

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

Add '55' to each side of the equation.
-55 + 55 + 4t2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 4t2 = 0 + 55
4t2 = 0 + 55

Combine like terms: 0 + 55 = 55
4t2 = 55

Divide each side by '4'.
t2 = 13.75

Simplifying
t2 = 13.75

Take the square root of each side:
t = {-3.708099244, 3.708099244}