f(0)=8x^2+53x-21

Solution for f(0)=8x^2+53x-21 equation:

Simplifying
f(0) = 8x2 + 53x + -21

Reorder the terms for easier multiplication:
0f = 8x2 + 53x + -21

Anything times zero is zero.
0f = 8x2 + 53x + -21

Reorder the terms:
0 = -21 + 53x + 8x2

Solving
0 = -21 + 53x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 21 = 21
21 + -53x + -8x2 = -21 + 53x + 8x2 + 21 + -53x + -8x2

Reorder the terms:
21 + -53x + -8x2 = -21 + 21 + 53x + -53x + 8x2 + -8x2

Combine like terms: -21 + 21 = 0
21 + -53x + -8x2 = 0 + 53x + -53x + 8x2 + -8x2
21 + -53x + -8x2 = 53x + -53x + 8x2 + -8x2

Combine like terms: 53x + -53x = 0
21 + -53x + -8x2 = 0 + 8x2 + -8x2
21 + -53x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
21 + -53x + -8x2 = 0

Factor a trinomial.
(3 + -8x)(7 + x) = 0

Subproblem 1
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0.375, -7}