2x^2+3x=10x+15

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Solution for 2x^2+3x=10x+15 equation: 


Simplifying
2x2 + 3x = 10x + 15

Reorder the terms:
3x + 2x2 = 10x + 15

Reorder the terms:
3x + 2x2 = 15 + 10x

Solving
3x + 2x2 = 15 + 10x

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + -10x + 2x2 = 15 + 10x + -15 + -10x

Combine like terms: 3x + -10x = -7x
-15 + -7x + 2x2 = 15 + 10x + -15 + -10x

Reorder the terms:
-15 + -7x + 2x2 = 15 + -15 + 10x + -10x

Combine like terms: 15 + -15 = 0
-15 + -7x + 2x2 = 0 + 10x + -10x
-15 + -7x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-15 + -7x + 2x2 = 0

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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, 5}

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