0=490t^2-1120t+640

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Solution for 0=490t^2-1120t+640 equation:


Simplifying
0 = 490t2 + -1120t + 640

Reorder the terms:
0 = 640 + -1120t + 490t2

Solving
0 = 640 + -1120t + 490t2

Solving for variable 't'.

Combine like terms: 0 + -640 = -640
-640 + 1120t + -490t2 = 640 + -1120t + 490t2 + -640 + 1120t + -490t2

Reorder the terms:
-640 + 1120t + -490t2 = 640 + -640 + -1120t + 1120t + 490t2 + -490t2

Combine like terms: 640 + -640 = 0
-640 + 1120t + -490t2 = 0 + -1120t + 1120t + 490t2 + -490t2
-640 + 1120t + -490t2 = -1120t + 1120t + 490t2 + -490t2

Combine like terms: -1120t + 1120t = 0
-640 + 1120t + -490t2 = 0 + 490t2 + -490t2
-640 + 1120t + -490t2 = 490t2 + -490t2

Combine like terms: 490t2 + -490t2 = 0
-640 + 1120t + -490t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-64 + 112t + -49t2) = 0

Factor a trinomial.
10((-8 + 7t)(8 + -7t)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-8 + 7t)' equal to zero and attempt to solve: Simplifying -8 + 7t = 0 Solving -8 + 7t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 7t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 7t = 0 + 8 7t = 0 + 8 Combine like terms: 0 + 8 = 8 7t = 8 Divide each side by '7'. t = 1.142857143 Simplifying t = 1.142857143

Subproblem 2

Set the factor '(8 + -7t)' equal to zero and attempt to solve: Simplifying 8 + -7t = 0 Solving 8 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7t = 0 + -8 -7t = 0 + -8 Combine like terms: 0 + -8 = -8 -7t = -8 Divide each side by '-7'. t = 1.142857143 Simplifying t = 1.142857143

Solution

t = {1.142857143, 1.142857143}

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