4x^2+x+6=-7x+3

Solution for 4x^2+x+6=-7x+3 equation:

Simplifying
4x2 + x + 6 = -7x + 3

Reorder the terms:
6 + x + 4x2 = -7x + 3

Reorder the terms:
6 + x + 4x2 = 3 + -7x

Solving
6 + x + 4x2 = 3 + -7x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + x + 7x + 4x2 = 3 + -7x + -3 + 7x

Combine like terms: 6 + -3 = 3
3 + x + 7x + 4x2 = 3 + -7x + -3 + 7x

Combine like terms: x + 7x = 8x
3 + 8x + 4x2 = 3 + -7x + -3 + 7x

Reorder the terms:
3 + 8x + 4x2 = 3 + -3 + -7x + 7x

Combine like terms: 3 + -3 = 0
3 + 8x + 4x2 = 0 + -7x + 7x
3 + 8x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
3 + 8x + 4x2 = 0

Factor a trinomial.
(3 + 2x)(1 + 2x) = 0

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, -0.5}