(3x-1)(x+3)=77

Solution for (3x-1)(x+3)=77 equation:

Simplifying
(3x + -1)(x + 3) = 77

Reorder the terms:
(-1 + 3x)(x + 3) = 77

Reorder the terms:
(-1 + 3x)(3 + x) = 77

Multiply (-1 + 3x) * (3 + x)
(-1(3 + x) + 3x * (3 + x)) = 77
((3 * -1 + x * -1) + 3x * (3 + x)) = 77
((-3 + -1x) + 3x * (3 + x)) = 77
(-3 + -1x + (3 * 3x + x * 3x)) = 77
(-3 + -1x + (9x + 3x2)) = 77

Combine like terms: -1x + 9x = 8x
(-3 + 8x + 3x2) = 77

Solving
-3 + 8x + 3x2 = 77

Solving for variable 'x'.

Reorder the terms:
-3 + -77 + 8x + 3x2 = 77 + -77

Combine like terms: -3 + -77 = -80
-80 + 8x + 3x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-80 + 8x + 3x2 = 0

Factor a trinomial.
(-20 + -3x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -3x)' equal to zero and attempt to solve:

Simplifying
-20 + -3x = 0

Solving
-20 + -3x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3x = 0 + 20
-3x = 0 + 20

Combine like terms: 0 + 20 = 20
-3x = 20

Divide each side by '-3'.
x = -6.666666667

Simplifying
x = -6.666666667
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6.666666667, 4}