9x^2-13x=8x-10

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Solution for 9x^2-13x=8x-10 equation: 


Simplifying
9x2 + -13x = 8x + -10

Reorder the terms:
-13x + 9x2 = 8x + -10

Reorder the terms:
-13x + 9x2 = -10 + 8x

Solving
-13x + 9x2 = -10 + 8x

Solving for variable 'x'.

Reorder the terms:
10 + -13x + -8x + 9x2 = -10 + 8x + 10 + -8x

Combine like terms: -13x + -8x = -21x
10 + -21x + 9x2 = -10 + 8x + 10 + -8x

Reorder the terms:
10 + -21x + 9x2 = -10 + 10 + 8x + -8x

Combine like terms: -10 + 10 = 0
10 + -21x + 9x2 = 0 + 8x + -8x
10 + -21x + 9x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
10 + -21x + 9x2 = 0

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


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

Simplifying
2 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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 = {0.6666666667, 1.666666667}

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