1000=50t+70t(t-2)

Solution for 1000=50t+70t(t-2) equation:

Simplifying
1000 = 50t + 70t(t + -2)

Reorder the terms:
1000 = 50t + 70t(-2 + t)
1000 = 50t + (-2 * 70t + t * 70t)
1000 = 50t + (-140t + 70t2)

Combine like terms: 50t + -140t = -90t
1000 = -90t + 70t2

Solving
1000 = -90t + 70t2

Solving for variable 't'.

Reorder the terms:
1000 + 90t + -70t2 = -90t + 90t + 70t2 + -70t2

Combine like terms: -90t + 90t = 0
1000 + 90t + -70t2 = 0 + 70t2 + -70t2
1000 + 90t + -70t2 = 70t2 + -70t2

Combine like terms: 70t2 + -70t2 = 0
1000 + 90t + -70t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(100 + 9t + -7t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(100 + 9t + -7t2)' equal to zero and attempt to solve:

Simplifying
100 + 9t + -7t2 = 0

Solving
100 + 9t + -7t2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-14.28571429 + -1.285714286t + t2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + -1.285714286t + 14.28571429 + t2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + -1.285714286t + t2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + -1.285714286t + t2 = 0 + 14.28571429
-1.285714286t + t2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
-1.285714286t + t2 = 14.28571429

The t term is -1.285714286t.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286t + 0.4132653063 + t2 = 14.28571429 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286t + t2 = 14.28571429 + 0.4132653063

Combine like terms: 14.28571429 + 0.4132653063 = 14.6989795963
0.4132653063 + -1.285714286t + t2 = 14.6989795963

Factor a perfect square on the left side:
(t + -0.642857143)(t + -0.642857143) = 14.6989795963

Calculate the square root of the right side: 3.833924829

Break this problem into two subproblems by setting 
(t + -0.642857143) equal to 3.833924829 and -3.833924829.

Subproblem 1
t + -0.642857143 = 3.833924829

Simplifying
t + -0.642857143 = 3.833924829

Reorder the terms:
-0.642857143 + t = 3.833924829

Solving
-0.642857143 + t = 3.833924829

Solving for variable 't'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + t = 3.833924829 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + t = 3.833924829 + 0.642857143
t = 3.833924829 + 0.642857143

Combine like terms: 3.833924829 + 0.642857143 = 4.476781972
t = 4.476781972

Simplifying
t = 4.476781972

Subproblem 2
t + -0.642857143 = -3.833924829

Simplifying
t + -0.642857143 = -3.833924829

Reorder the terms:
-0.642857143 + t = -3.833924829

Solving
-0.642857143 + t = -3.833924829

Solving for variable 't'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + t = -3.833924829 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + t = -3.833924829 + 0.642857143
t = -3.833924829 + 0.642857143

Combine like terms: -3.833924829 + 0.642857143 = -3.191067686
t = -3.191067686

Simplifying
t = -3.191067686

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.476781972, -3.191067686}
Solution
t = {4.476781972, -3.191067686}