4x+5x^2-10=3x+2x^2

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Solution for 4x+5x^2-10=3x+2x^2 equation: 


Simplifying
4x + 5x2 + -10 = 3x + 2x2

Reorder the terms:
-10 + 4x + 5x2 = 3x + 2x2

Solving
-10 + 4x + 5x2 = 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 4x + -3x + 5x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: 4x + -3x = 1x
-10 + 1x + 5x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-10 + 1x + 3x2 = 3x + 2x2 + -3x + -2x2

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

Combine like terms: 3x + -3x = 0
-10 + 1x + 3x2 = 0 + 2x2 + -2x2
-10 + 1x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 1x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -3x) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-2, 1.666666667}

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