(4t+2)(5t-7)=0

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Solution for (4t+2)(5t-7)=0 equation: 


Simplifying
(4t + 2)(5t + -7) = 0

Reorder the terms:
(2 + 4t)(5t + -7) = 0

Reorder the terms:
(2 + 4t)(-7 + 5t) = 0

Multiply (2 + 4t) * (-7 + 5t)
(2(-7 + 5t) + 4t * (-7 + 5t)) = 0
((-7 * 2 + 5t * 2) + 4t * (-7 + 5t)) = 0
((-14 + 10t) + 4t * (-7 + 5t)) = 0
(-14 + 10t + (-7 * 4t + 5t * 4t)) = 0
(-14 + 10t + (-28t + 20t2)) = 0

Combine like terms: 10t + -28t = -18t
(-14 + -18t + 20t2) = 0

Solving
-14 + -18t + 20t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -9t + 10t2) = 0

Factor a trinomial.
2((-1 + -2t)(7 + -5t)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -2t = 0

Solving
-1 + -2t = 0

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

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

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

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

Divide each side by '-2'.
t = -0.5

Simplifying
t = -0.5

Subproblem 2
Set the factor '(7 + -5t)' equal to zero and attempt to solve:

Simplifying
7 + -5t = 0

Solving
7 + -5t = 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 + -5t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5t = 0 + -7
-5t = 0 + -7

Combine like terms: 0 + -7 = -7
-5t = -7

Divide each side by '-5'.
t = 1.4

Simplifying
t = 1.4
Solution
t = {-0.5, 1.4}

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