(5x^2-9x+1)-(8x+13)=0

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Solution for (5x^2-9x+1)-(8x+13)=0 equation: 


Simplifying
(5x2 + -9x + 1) + -1(8x + 13) = 0

Reorder the terms:
(1 + -9x + 5x2) + -1(8x + 13) = 0

Remove parenthesis around (1 + -9x + 5x2)
1 + -9x + 5x2 + -1(8x + 13) = 0

Reorder the terms:
1 + -9x + 5x2 + -1(13 + 8x) = 0
1 + -9x + 5x2 + (13 * -1 + 8x * -1) = 0
1 + -9x + 5x2 + (-13 + -8x) = 0

Reorder the terms:
1 + -13 + -9x + -8x + 5x2 = 0

Combine like terms: 1 + -13 = -12
-12 + -9x + -8x + 5x2 = 0

Combine like terms: -9x + -8x = -17x
-12 + -17x + 5x2 = 0

Solving
-12 + -17x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

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

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

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.6, 4}

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