(4t+2)(t-3)=

Solution for (4t+2)(t-3)= equation:

Simplifying
(4t + 2)(t + -3) = 0

Reorder the terms:
(2 + 4t)(t + -3) = 0

Reorder the terms:
(2 + 4t)(-3 + t) = 0

Multiply (2 + 4t) * (-3 + t)
(2(-3 + t) + 4t * (-3 + t)) = 0
((-3 * 2 + t * 2) + 4t * (-3 + t)) = 0
((-6 + 2t) + 4t * (-3 + t)) = 0
(-6 + 2t + (-3 * 4t + t * 4t)) = 0
(-6 + 2t + (-12t + 4t2)) = 0

Combine like terms: 2t + -12t = -10t
(-6 + -10t + 4t2) = 0

Solving
-6 + -10t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5t + 2t2) = 0

Factor a trinomial.
2((-1 + -2t)(3 + -1t)) = 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 '(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 = {-0.5, 3}