4x^2-10x+6=2x^2+x-3

Solution for 4x^2-10x+6=2x^2+x-3 equation:

Simplifying
4x2 + -10x + 6 = 2x2 + x + -3

Reorder the terms:
6 + -10x + 4x2 = 2x2 + x + -3

Reorder the terms:
6 + -10x + 4x2 = -3 + x + 2x2

Solving
6 + -10x + 4x2 = -3 + x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + 3 + -10x + -1x + 4x2 + -2x2 = -3 + x + 2x2 + 3 + -1x + -2x2

Combine like terms: 6 + 3 = 9
9 + -10x + -1x + 4x2 + -2x2 = -3 + x + 2x2 + 3 + -1x + -2x2

Combine like terms: -10x + -1x = -11x
9 + -11x + 4x2 + -2x2 = -3 + x + 2x2 + 3 + -1x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
9 + -11x + 2x2 = -3 + x + 2x2 + 3 + -1x + -2x2

Reorder the terms:
9 + -11x + 2x2 = -3 + 3 + x + -1x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
9 + -11x + 2x2 = 0 + x + -1x + 2x2 + -2x2
9 + -11x + 2x2 = x + -1x + 2x2 + -2x2

Combine like terms: x + -1x = 0
9 + -11x + 2x2 = 0 + 2x2 + -2x2
9 + -11x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
9 + -11x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -2x) = 0

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1, 4.5}