4(3t+7)(t-3)=

Solution for 4(3t+7)(t-3)= equation:

Simplifying
4(3t + 7)(t + -3) = 0

Reorder the terms:
4(7 + 3t)(t + -3) = 0

Reorder the terms:
4(7 + 3t)(-3 + t) = 0

Multiply (7 + 3t) * (-3 + t)
4(7(-3 + t) + 3t * (-3 + t)) = 0
4((-3 * 7 + t * 7) + 3t * (-3 + t)) = 0
4((-21 + 7t) + 3t * (-3 + t)) = 0
4(-21 + 7t + (-3 * 3t + t * 3t)) = 0
4(-21 + 7t + (-9t + 3t2)) = 0

Combine like terms: 7t + -9t = -2t
4(-21 + -2t + 3t2) = 0
(-21 * 4 + -2t * 4 + 3t2 * 4) = 0
(-84 + -8t + 12t2) = 0

Solving
-84 + -8t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -2t + 3t2) = 0

Factor a trinomial.
4((-7 + -3t)(3 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -3t)' equal to zero and attempt to solve:

Simplifying
-7 + -3t = 0

Solving
-7 + -3t = 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 + -3t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3t = 0 + 7
-3t = 0 + 7

Combine like terms: 0 + 7 = 7
-3t = 7

Divide each side by '-3'.
t = -2.333333333

Simplifying
t = -2.333333333
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 = {-2.333333333, 3}