4x^2+74x-78=0

Solution for 4x^2+74x-78=0 equation:

Simplifying
4x2 + 74x + -78 = 0

Reorder the terms:
-78 + 74x + 4x2 = 0

Solving
-78 + 74x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + 37x + 2x2) = 0

Factor a trinomial.
2((-39 + -2x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-39 + -2x)' equal to zero and attempt to solve:

Simplifying
-39 + -2x = 0

Solving
-39 + -2x = 0

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

Add '39' to each side of the equation.
-39 + 39 + -2x = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -2x = 0 + 39
-2x = 0 + 39

Combine like terms: 0 + 39 = 39
-2x = 39

Divide each side by '-2'.
x = -19.5

Simplifying
x = -19.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-19.5, 1}