2t(t-5)-t^2=t^2+30

Solution for 2t(t-5)-t^2=t^2+30 equation:

Simplifying
2t(t + -5) + -1t2 = t2 + 30

Reorder the terms:
2t(-5 + t) + -1t2 = t2 + 30
(-5 * 2t + t * 2t) + -1t2 = t2 + 30
(-10t + 2t2) + -1t2 = t2 + 30

Combine like terms: 2t2 + -1t2 = 1t2
-10t + 1t2 = t2 + 30

Reorder the terms:
-10t + 1t2 = 30 + t2

Solving
-10t + 1t2 = 30 + t2

Solving for variable 't'.

Reorder the terms:
-30 + -10t + 1t2 + -1t2 = 30 + t2 + -30 + -1t2

Combine like terms: 1t2 + -1t2 = 0
-30 + -10t + 0 = 30 + t2 + -30 + -1t2
-30 + -10t = 30 + t2 + -30 + -1t2

Reorder the terms:
-30 + -10t = 30 + -30 + t2 + -1t2

Combine like terms: 30 + -30 = 0
-30 + -10t = 0 + t2 + -1t2
-30 + -10t = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-30 + -10t = 0

Factor out the Greatest Common Factor (GCF), '-10'.
-10(3 + t) = 0

Ignore the factor -10.
Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {-3}