4x^2+76x+312=680

Solution for 4x^2+76x+312=680 equation:

Simplifying
4x2 + 76x + 312 = 680

Reorder the terms:
312 + 76x + 4x2 = 680

Solving
312 + 76x + 4x2 = 680

Solving for variable 'x'.

Reorder the terms:
312 + -680 + 76x + 4x2 = 680 + -680

Combine like terms: 312 + -680 = -368
-368 + 76x + 4x2 = 680 + -680

Combine like terms: 680 + -680 = 0
-368 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-92 + 19x + x2) = 0

Factor a trinomial.
4((-23 + -1x)(4 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve:

Simplifying
-23 + -1x = 0

Solving
-23 + -1x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 0 + 23
-1x = 0 + 23

Combine like terms: 0 + 23 = 23
-1x = 23

Divide each side by '-1'.
x = -23

Simplifying
x = -23
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 = {-23, 4}