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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -5x + -3x = -8x
-10 + -8x + 2x2 = 10 + 3x + -10 + -3x

Reorder the terms:
-10 + -8x + 2x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
-10 + -8x + 2x2 = 0 + 3x + -3x
-10 + -8x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + x2) = 0

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

Ignore the factor 2.

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 '(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 = {-1, 5}

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