4x^2+2x-156=0

Solution for 4x^2+2x-156=0 equation:

Simplifying
4x2 + 2x + -156 = 0

Reorder the terms:
-156 + 2x + 4x2 = 0

Solving
-156 + 2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + x + 2x2) = 0

Factor a trinomial.
2((-13 + -2x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
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 = {-6.5, 6}