x^2-5x=-7x+3

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Solution for x^2-5x=-7x+3 equation:


Simplifying
x2 + -5x = -7x + 3

Reorder the terms:
-5x + x2 = -7x + 3

Reorder the terms:
-5x + x2 = 3 + -7x

Solving
-5x + x2 = 3 + -7x

Solving for variable 'x'.

Reorder the terms:
-3 + -5x + 7x + x2 = 3 + -7x + -3 + 7x

Combine like terms: -5x + 7x = 2x
-3 + 2x + x2 = 3 + -7x + -3 + 7x

Reorder the terms:
-3 + 2x + x2 = 3 + -3 + -7x + 7x

Combine like terms: 3 + -3 = 0
-3 + 2x + x2 = 0 + -7x + 7x
-3 + 2x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 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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