0=4x^2+25x+21

Solution for 0=4x^2+25x+21 equation:

Simplifying
0 = 4x2 + 25x + 21

Reorder the terms:
0 = 21 + 25x + 4x2

Solving
0 = 21 + 25x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -21 = -21
-21 + -25x + -4x2 = 21 + 25x + 4x2 + -21 + -25x + -4x2

Reorder the terms:
-21 + -25x + -4x2 = 21 + -21 + 25x + -25x + 4x2 + -4x2

Combine like terms: 21 + -21 = 0
-21 + -25x + -4x2 = 0 + 25x + -25x + 4x2 + -4x2
-21 + -25x + -4x2 = 25x + -25x + 4x2 + -4x2

Combine like terms: 25x + -25x = 0
-21 + -25x + -4x2 = 0 + 4x2 + -4x2
-21 + -25x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-21 + -25x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 25x + 4x2) = 0

Factor a trinomial.
-1((21 + 4x)(1 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 4x)' equal to zero and attempt to solve:

Simplifying
21 + 4x = 0

Solving
21 + 4x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 4x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4x = 0 + -21
4x = 0 + -21

Combine like terms: 0 + -21 = -21
4x = -21

Divide each side by '4'.
x = -5.25

Simplifying
x = -5.25
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-5.25, -1}