(10t+7)(3t-9)=0

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Solution for (10t+7)(3t-9)=0 equation: 


Simplifying
(10t + 7)(3t + -9) = 0

Reorder the terms:
(7 + 10t)(3t + -9) = 0

Reorder the terms:
(7 + 10t)(-9 + 3t) = 0

Multiply (7 + 10t) * (-9 + 3t)
(7(-9 + 3t) + 10t * (-9 + 3t)) = 0
((-9 * 7 + 3t * 7) + 10t * (-9 + 3t)) = 0
((-63 + 21t) + 10t * (-9 + 3t)) = 0
(-63 + 21t + (-9 * 10t + 3t * 10t)) = 0
(-63 + 21t + (-90t + 30t2)) = 0

Combine like terms: 21t + -90t = -69t
(-63 + -69t + 30t2) = 0

Solving
-63 + -69t + 30t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -23t + 10t2) = 0

Factor a trinomial.
3((-7 + -10t)(3 + -1t)) = 0

Ignore the factor 3.

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

Simplifying
-7 + -10t = 0

Solving
-7 + -10t = 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 + -10t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10t = 0 + 7
-10t = 0 + 7

Combine like terms: 0 + 7 = 7
-10t = 7

Divide each side by '-10'.
t = -0.7

Simplifying
t = -0.7

Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.7, 3}

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