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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -6x + -1x = -7x
10 + -7x + 4x2 + -3x2 = -10 + x + 3x2 + 10 + -1x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
10 + -7x + 1x2 = -10 + x + 3x2 + 10 + -1x + -3x2

Reorder the terms:
10 + -7x + 1x2 = -10 + 10 + x + -1x + 3x2 + -3x2

Combine like terms: -10 + 10 = 0
10 + -7x + 1x2 = 0 + x + -1x + 3x2 + -3x2
10 + -7x + 1x2 = x + -1x + 3x2 + -3x2

Combine like terms: x + -1x = 0
10 + -7x + 1x2 = 0 + 3x2 + -3x2
10 + -7x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + -7x + 1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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