0=4x^2+67x+258

Solution for 0=4x^2+67x+258 equation:

Simplifying
0 = 4x2 + 67x + 258

Reorder the terms:
0 = 258 + 67x + 4x2

Solving
0 = 258 + 67x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -258 = -258
-258 + -67x + -4x2 = 258 + 67x + 4x2 + -258 + -67x + -4x2

Reorder the terms:
-258 + -67x + -4x2 = 258 + -258 + 67x + -67x + 4x2 + -4x2

Combine like terms: 258 + -258 = 0
-258 + -67x + -4x2 = 0 + 67x + -67x + 4x2 + -4x2
-258 + -67x + -4x2 = 67x + -67x + 4x2 + -4x2

Combine like terms: 67x + -67x = 0
-258 + -67x + -4x2 = 0 + 4x2 + -4x2
-258 + -67x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-258 + -67x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(258 + 67x + 4x2) = 0

Factor a trinomial.
-1((43 + 4x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(43 + 4x)' equal to zero and attempt to solve:

Simplifying
43 + 4x = 0

Solving
43 + 4x = 0

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

Add '-43' to each side of the equation.
43 + -43 + 4x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 4x = 0 + -43
4x = 0 + -43

Combine like terms: 0 + -43 = -43
4x = -43

Divide each side by '4'.
x = -10.75

Simplifying
x = -10.75
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-10.75, -6}