4x^2+46x-420=0

Solution for 4x^2+46x-420=0 equation:

Simplifying
4x2 + 46x + -420 = 0

Reorder the terms:
-420 + 46x + 4x2 = 0

Solving
-420 + 46x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + 23x + 2x2) = 0

Factor a trinomial.
2((-35 + -2x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -2x)' equal to zero and attempt to solve:

Simplifying
-35 + -2x = 0

Solving
-35 + -2x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -2x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -2x = 0 + 35
-2x = 0 + 35

Combine like terms: 0 + 35 = 35
-2x = 35

Divide each side by '-2'.
x = -17.5

Simplifying
x = -17.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-17.5, 6}