10x^2+20x-77=3

Solution for 10x^2+20x-77=3 equation:

Simplifying
10x2 + 20x + -77 = 3

Reorder the terms:
-77 + 20x + 10x2 = 3

Solving
-77 + 20x + 10x2 = 3

Solving for variable 'x'.

Reorder the terms:
-77 + -3 + 20x + 10x2 = 3 + -3

Combine like terms: -77 + -3 = -80
-80 + 20x + 10x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-80 + 20x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 2x + x2) = 0

Factor a trinomial.
10((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}