4x^2+13x+3=x+3

Solution for 4x^2+13x+3=x+3 equation:

Simplifying
4x2 + 13x + 3 = x + 3

Reorder the terms:
3 + 13x + 4x2 = x + 3

Reorder the terms:
3 + 13x + 4x2 = 3 + x

Add '-3' to each side of the equation.
3 + 13x + -3 + 4x2 = 3 + -3 + x

Reorder the terms:
3 + -3 + 13x + 4x2 = 3 + -3 + x

Combine like terms: 3 + -3 = 0
0 + 13x + 4x2 = 3 + -3 + x
13x + 4x2 = 3 + -3 + x

Combine like terms: 3 + -3 = 0
13x + 4x2 = 0 + x
13x + 4x2 = x

Solving
13x + 4x2 = x

Solving for variable 'x'.

Reorder the terms:
13x + -1x + 4x2 = x + -1x

Combine like terms: 13x + -1x = 12x
12x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
12x + 4x2 = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {0, -3}