10=15t^2+25t-100

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Solution for 10=15t^2+25t-100 equation: 


Simplifying
10 = 15t2 + 25t + -100

Reorder the terms:
10 = -100 + 25t + 15t2

Solving
10 = -100 + 25t + 15t2

Solving for variable 't'.

Combine like terms: 10 + 100 = 110
110 + -25t + -15t2 = -100 + 25t + 15t2 + 100 + -25t + -15t2

Reorder the terms:
110 + -25t + -15t2 = -100 + 100 + 25t + -25t + 15t2 + -15t2

Combine like terms: -100 + 100 = 0
110 + -25t + -15t2 = 0 + 25t + -25t + 15t2 + -15t2
110 + -25t + -15t2 = 25t + -25t + 15t2 + -15t2

Combine like terms: 25t + -25t = 0
110 + -25t + -15t2 = 0 + 15t2 + -15t2
110 + -25t + -15t2 = 15t2 + -15t2

Combine like terms: 15t2 + -15t2 = 0
110 + -25t + -15t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(22 + -5t + -3t2) = 0

Factor a trinomial.
5((2 + -1t)(11 + 3t)) = 0

Ignore the factor 5.

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2

Subproblem 2
Set the factor '(11 + 3t)' equal to zero and attempt to solve:

Simplifying
11 + 3t = 0

Solving
11 + 3t = 0

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

Add '-11' to each side of the equation.
11 + -11 + 3t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3t = 0 + -11
3t = 0 + -11

Combine like terms: 0 + -11 = -11
3t = -11

Divide each side by '3'.
t = -3.666666667

Simplifying
t = -3.666666667
Solution
t = {2, -3.666666667}

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