0=4(2x^2+3x+1)

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Solution for 0=4(2x^2+3x+1) equation: 


Simplifying
0 = 4(2x2 + 3x + 1)

Reorder the terms:
0 = 4(1 + 3x + 2x2)
0 = (1 * 4 + 3x * 4 + 2x2 * 4)
0 = (4 + 12x + 8x2)

Solving
0 = 4 + 12x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -12x + -8x2 = 4 + 12x + 8x2 + -4 + -12x + -8x2

Reorder the terms:
-4 + -12x + -8x2 = 4 + -4 + 12x + -12x + 8x2 + -8x2

Combine like terms: 4 + -4 = 0
-4 + -12x + -8x2 = 0 + 12x + -12x + 8x2 + -8x2
-4 + -12x + -8x2 = 12x + -12x + 8x2 + -8x2

Combine like terms: 12x + -12x = 0
-4 + -12x + -8x2 = 0 + 8x2 + -8x2
-4 + -12x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-4 + -12x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(1 + 3x + 2x2) = 0

Factor a trinomial.
-4((1 + x)(1 + 2x)) = 0

Ignore the factor -4.

Subproblem 1
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

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1, -0.5}

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