x^2+4x=10x-9

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Solution for x^2+4x=10x-9 equation:


Simplifying
x2 + 4x = 10x + -9

Reorder the terms:
4x + x2 = 10x + -9

Reorder the terms:
4x + x2 = -9 + 10x

Solving
4x + x2 = -9 + 10x

Solving for variable 'x'.

Reorder the terms:
9 + 4x + -10x + x2 = -9 + 10x + 9 + -10x

Combine like terms: 4x + -10x = -6x
9 + -6x + x2 = -9 + 10x + 9 + -10x

Reorder the terms:
9 + -6x + x2 = -9 + 9 + 10x + -10x

Combine like terms: -9 + 9 = 0
9 + -6x + x2 = 0 + 10x + -10x
9 + -6x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
9 + -6x + x2 = 0

Factor a trinomial.
(3 + -1x)(3 + -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 '(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 = {3, 3}

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