4x^2+17x+10=x-2

Solution for 4x^2+17x+10=x-2 equation:

Simplifying
4x2 + 17x + 10 = x + -2

Reorder the terms:
10 + 17x + 4x2 = x + -2

Reorder the terms:
10 + 17x + 4x2 = -2 + x

Solving
10 + 17x + 4x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
10 + 2 + 17x + -1x + 4x2 = -2 + x + 2 + -1x

Combine like terms: 10 + 2 = 12
12 + 17x + -1x + 4x2 = -2 + x + 2 + -1x

Combine like terms: 17x + -1x = 16x
12 + 16x + 4x2 = -2 + x + 2 + -1x

Reorder the terms:
12 + 16x + 4x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
12 + 16x + 4x2 = 0 + x + -1x
12 + 16x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
12 + 16x + 4x2 = 0

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

Factor a trinomial.
4((3 + x)(1 + x)) = 0

Ignore the factor 4.
Subproblem 1
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
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 = {-3, -1}