0=4x^2+17x+4

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Solution for 0=4x^2+17x+4 equation: 


Simplifying
0 = 4x2 + 17x + 4

Reorder the terms:
0 = 4 + 17x + 4x2

Solving
0 = 4 + 17x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -17x + -4x2 = 4 + 17x + 4x2 + -4 + -17x + -4x2

Reorder the terms:
-4 + -17x + -4x2 = 4 + -4 + 17x + -17x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
-4 + -17x + -4x2 = 0 + 17x + -17x + 4x2 + -4x2
-4 + -17x + -4x2 = 17x + -17x + 4x2 + -4x2

Combine like terms: 17x + -17x = 0
-4 + -17x + -4x2 = 0 + 4x2 + -4x2
-4 + -17x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + -17x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 17x + 4x2) = 0

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

Ignore the factor -1.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-4, -0.25}

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