5x^2+3x=6+10x

Solution for 5x^2+3x=6+10x equation:

Simplifying
5x2 + 3x = 6 + 10x

Reorder the terms:
3x + 5x2 = 6 + 10x

Solving
3x + 5x2 = 6 + 10x

Solving for variable 'x'.

Reorder the terms:
-6 + 3x + -10x + 5x2 = 6 + 10x + -6 + -10x

Combine like terms: 3x + -10x = -7x
-6 + -7x + 5x2 = 6 + 10x + -6 + -10x

Reorder the terms:
-6 + -7x + 5x2 = 6 + -6 + 10x + -10x

Combine like terms: 6 + -6 = 0
-6 + -7x + 5x2 = 0 + 10x + -10x
-6 + -7x + 5x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-6 + -7x + 5x2 = 0

Factor a trinomial.
(-3 + -5x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.6, 2}