4000t^2-28000t+3000=150000

Solution for 4000t^2-28000t+3000=150000 equation:

Simplifying
4000t2 + -28000t + 3000 = 150000

Reorder the terms:
3000 + -28000t + 4000t2 = 150000

Solving
3000 + -28000t + 4000t2 = 150000

Solving for variable 't'.

Reorder the terms:
3000 + -150000 + -28000t + 4000t2 = 150000 + -150000

Combine like terms: 3000 + -150000 = -147000
-147000 + -28000t + 4000t2 = 150000 + -150000

Combine like terms: 150000 + -150000 = 0
-147000 + -28000t + 4000t2 = 0

Factor out the Greatest Common Factor (GCF), '1000'.
1000(-147 + -28t + 4t2) = 0

Factor a trinomial.
1000((-7 + -2t)(21 + -2t)) = 0

Ignore the factor 1000.
Subproblem 1
Set the factor '(-7 + -2t)' equal to zero and attempt to solve:

Simplifying
-7 + -2t = 0

Solving
-7 + -2t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2t = 0 + 7
-2t = 0 + 7

Combine like terms: 0 + 7 = 7
-2t = 7

Divide each side by '-2'.
t = -3.5

Simplifying
t = -3.5
Subproblem 2
Set the factor '(21 + -2t)' equal to zero and attempt to solve:

Simplifying
21 + -2t = 0

Solving
21 + -2t = 0

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

Add '-21' to each side of the equation.
21 + -21 + -2t = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2t = 0 + -21
-2t = 0 + -21

Combine like terms: 0 + -21 = -21
-2t = -21

Divide each side by '-2'.
t = 10.5

Simplifying
t = 10.5
Solution
t = {-3.5, 10.5}