f(0)=4x^2+29x+30

Solution for f(0)=4x^2+29x+30 equation:

Simplifying
f(0) = 4x2 + 29x + 30

Reorder the terms for easier multiplication:
0f = 4x2 + 29x + 30

Anything times zero is zero.
0f = 4x2 + 29x + 30

Reorder the terms:
0 = 30 + 29x + 4x2

Solving
0 = 30 + 29x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -30 = -30
-30 + -29x + -4x2 = 30 + 29x + 4x2 + -30 + -29x + -4x2

Reorder the terms:
-30 + -29x + -4x2 = 30 + -30 + 29x + -29x + 4x2 + -4x2

Combine like terms: 30 + -30 = 0
-30 + -29x + -4x2 = 0 + 29x + -29x + 4x2 + -4x2
-30 + -29x + -4x2 = 29x + -29x + 4x2 + -4x2

Combine like terms: 29x + -29x = 0
-30 + -29x + -4x2 = 0 + 4x2 + -4x2
-30 + -29x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-30 + -29x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 29x + 4x2) = 0

Factor a trinomial.
-1((6 + x)(5 + 4x)) = 0

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-6, -1.25}