10x^2+20x+3=x-3

Solution for 10x^2+20x+3=x-3 equation:

Simplifying
10x2 + 20x + 3 = x + -3

Reorder the terms:
3 + 20x + 10x2 = x + -3

Reorder the terms:
3 + 20x + 10x2 = -3 + x

Solving
3 + 20x + 10x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
3 + 3 + 20x + -1x + 10x2 = -3 + x + 3 + -1x

Combine like terms: 3 + 3 = 6
6 + 20x + -1x + 10x2 = -3 + x + 3 + -1x

Combine like terms: 20x + -1x = 19x
6 + 19x + 10x2 = -3 + x + 3 + -1x

Reorder the terms:
6 + 19x + 10x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
6 + 19x + 10x2 = 0 + x + -1x
6 + 19x + 10x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 19x + 10x2 = 0

Factor a trinomial.
(3 + 2x)(2 + 5x) = 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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-1.5, -0.4}