8x^2-3x-13=5x^2+2x-1

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Solution for 8x^2-3x-13=5x^2+2x-1 equation: 


Simplifying
8x2 + -3x + -13 = 5x2 + 2x + -1

Reorder the terms:
-13 + -3x + 8x2 = 5x2 + 2x + -1

Reorder the terms:
-13 + -3x + 8x2 = -1 + 2x + 5x2

Solving
-13 + -3x + 8x2 = -1 + 2x + 5x2

Solving for variable 'x'.

Reorder the terms:
-13 + 1 + -3x + -2x + 8x2 + -5x2 = -1 + 2x + 5x2 + 1 + -2x + -5x2

Combine like terms: -13 + 1 = -12
-12 + -3x + -2x + 8x2 + -5x2 = -1 + 2x + 5x2 + 1 + -2x + -5x2

Combine like terms: -3x + -2x = -5x
-12 + -5x + 8x2 + -5x2 = -1 + 2x + 5x2 + 1 + -2x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-12 + -5x + 3x2 = -1 + 2x + 5x2 + 1 + -2x + -5x2

Reorder the terms:
-12 + -5x + 3x2 = -1 + 1 + 2x + -2x + 5x2 + -5x2

Combine like terms: -1 + 1 = 0
-12 + -5x + 3x2 = 0 + 2x + -2x + 5x2 + -5x2
-12 + -5x + 3x2 = 2x + -2x + 5x2 + -5x2

Combine like terms: 2x + -2x = 0
-12 + -5x + 3x2 = 0 + 5x2 + -5x2
-12 + -5x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-12 + -5x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.333333333, 3}

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