6x^2-10x=3x+5

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Solution for 6x^2-10x=3x+5 equation: 


Simplifying
6x2 + -10x = 3x + 5

Reorder the terms:
-10x + 6x2 = 3x + 5

Reorder the terms:
-10x + 6x2 = 5 + 3x

Solving
-10x + 6x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + -10x + -3x + 6x2 = 5 + 3x + -5 + -3x

Combine like terms: -10x + -3x = -13x
-5 + -13x + 6x2 = 5 + 3x + -5 + -3x

Reorder the terms:
-5 + -13x + 6x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
-5 + -13x + 6x2 = 0 + 3x + -3x
-5 + -13x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + -13x + 6x2 = 0

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


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.3333333333, 2.5}

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