2x^2+6x-77=3

Solution for 2x^2+6x-77=3 equation:

Simplifying
2x2 + 6x + -77 = 3

Reorder the terms:
-77 + 6x + 2x2 = 3

Solving
-77 + 6x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-77 + -3 + 6x + 2x2 = 3 + -3

Combine like terms: -77 + -3 = -80
-80 + 6x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-80 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 3x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-8, 5}