4(t-2)(t+22)=0

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Solution for 4(t-2)(t+22)=0 equation: 


Simplifying
4(t + -2)(t + 22) = 0

Reorder the terms:
4(-2 + t)(t + 22) = 0

Reorder the terms:
4(-2 + t)(22 + t) = 0

Multiply (-2 + t) * (22 + t)
4(-2(22 + t) + t(22 + t)) = 0
4((22 * -2 + t * -2) + t(22 + t)) = 0
4((-44 + -2t) + t(22 + t)) = 0
4(-44 + -2t + (22 * t + t * t)) = 0
4(-44 + -2t + (22t + t2)) = 0

Combine like terms: -2t + 22t = 20t
4(-44 + 20t + t2) = 0
(-44 * 4 + 20t * 4 + t2 * 4) = 0
(-176 + 80t + 4t2) = 0

Solving
-176 + 80t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-44 + 20t + t2) = 0

Factor a trinomial.
4((-22 + -1t)(2 + -1t)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-22 + -1t)' equal to zero and attempt to solve:

Simplifying
-22 + -1t = 0

Solving
-22 + -1t = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1t = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1t = 0 + 22
-1t = 0 + 22

Combine like terms: 0 + 22 = 22
-1t = 22

Divide each side by '-1'.
t = -22

Simplifying
t = -22

Subproblem 2
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
Solution
t = {-22, 2}

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