2x^2+17x=6x+21

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Solution for 2x^2+17x=6x+21 equation:


Simplifying
2x2 + 17x = 6x + 21

Reorder the terms:
17x + 2x2 = 6x + 21

Reorder the terms:
17x + 2x2 = 21 + 6x

Solving
17x + 2x2 = 21 + 6x

Solving for variable 'x'.

Reorder the terms:
-21 + 17x + -6x + 2x2 = 21 + 6x + -21 + -6x

Combine like terms: 17x + -6x = 11x
-21 + 11x + 2x2 = 21 + 6x + -21 + -6x

Reorder the terms:
-21 + 11x + 2x2 = 21 + -21 + 6x + -6x

Combine like terms: 21 + -21 = 0
-21 + 11x + 2x2 = 0 + 6x + -6x
-21 + 11x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-21 + 11x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -2x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-7, 1.5}

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