x^2+10x-8=8x-5

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Solution for x^2+10x-8=8x-5 equation:


Simplifying
x2 + 10x + -8 = 8x + -5

Reorder the terms:
-8 + 10x + x2 = 8x + -5

Reorder the terms:
-8 + 10x + x2 = -5 + 8x

Solving
-8 + 10x + x2 = -5 + 8x

Solving for variable 'x'.

Reorder the terms:
-8 + 5 + 10x + -8x + x2 = -5 + 8x + 5 + -8x

Combine like terms: -8 + 5 = -3
-3 + 10x + -8x + x2 = -5 + 8x + 5 + -8x

Combine like terms: 10x + -8x = 2x
-3 + 2x + x2 = -5 + 8x + 5 + -8x

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

Combine like terms: -5 + 5 = 0
-3 + 2x + x2 = 0 + 8x + -8x
-3 + 2x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-3 + 2x + x2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-3, 1}

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