(t-1)(5t+2)=

Solution for (t-1)(5t+2)= equation:

Simplifying
(t + -1)(5t + 2) = 0

Reorder the terms:
(-1 + t)(5t + 2) = 0

Reorder the terms:
(-1 + t)(2 + 5t) = 0

Multiply (-1 + t) * (2 + 5t)
(-1(2 + 5t) + t(2 + 5t)) = 0
((2 * -1 + 5t * -1) + t(2 + 5t)) = 0
((-2 + -5t) + t(2 + 5t)) = 0
(-2 + -5t + (2 * t + 5t * t)) = 0
(-2 + -5t + (2t + 5t2)) = 0

Combine like terms: -5t + 2t = -3t
(-2 + -3t + 5t2) = 0

Solving
-2 + -3t + 5t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(-2 + -5t)' equal to zero and attempt to solve:

Simplifying
-2 + -5t = 0

Solving
-2 + -5t = 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 + -5t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5t = 0 + 2
-5t = 0 + 2

Combine like terms: 0 + 2 = 2
-5t = 2

Divide each side by '-5'.
t = -0.4

Simplifying
t = -0.4
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

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

Simplifying
t = 1
Solution
t = {-0.4, 1}