t^2-4t=28-7t

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Solution for t^2-4t=28-7t equation:


Simplifying
t2 + -4t = 28 + -7t

Reorder the terms:
-4t + t2 = 28 + -7t

Solving
-4t + t2 = 28 + -7t

Solving for variable 't'.

Reorder the terms:
-28 + -4t + 7t + t2 = 28 + -7t + -28 + 7t

Combine like terms: -4t + 7t = 3t
-28 + 3t + t2 = 28 + -7t + -28 + 7t

Reorder the terms:
-28 + 3t + t2 = 28 + -28 + -7t + 7t

Combine like terms: 28 + -28 = 0
-28 + 3t + t2 = 0 + -7t + 7t
-28 + 3t + t2 = -7t + 7t

Combine like terms: -7t + 7t = 0
-28 + 3t + t2 = 0

Factor a trinomial.
(-7 + -1t)(4 + -1t) = 0

Subproblem 1

Set the factor '(-7 + -1t)' equal to zero and attempt to solve: Simplifying -7 + -1t = 0 Solving -7 + -1t = 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 + -1t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t = 0 + 7 -1t = 0 + 7 Combine like terms: 0 + 7 = 7 -1t = 7 Divide each side by '-1'. t = -7 Simplifying t = -7

Subproblem 2

Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Solution

t = {-7, 4}

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