x(5x+8)=2x^2-17x+18

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Solution for x(5x+8)=2x^2-17x+18 equation:


Simplifying
x(5x + 8) = 2x2 + -17x + 18

Reorder the terms:
x(8 + 5x) = 2x2 + -17x + 18
(8 * x + 5x * x) = 2x2 + -17x + 18
(8x + 5x2) = 2x2 + -17x + 18

Reorder the terms:
8x + 5x2 = 18 + -17x + 2x2

Solving
8x + 5x2 = 18 + -17x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 8x + 17x + 5x2 + -2x2 = 18 + -17x + 2x2 + -18 + 17x + -2x2

Combine like terms: 8x + 17x = 25x
-18 + 25x + 5x2 + -2x2 = 18 + -17x + 2x2 + -18 + 17x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-18 + 25x + 3x2 = 18 + -17x + 2x2 + -18 + 17x + -2x2

Reorder the terms:
-18 + 25x + 3x2 = 18 + -18 + -17x + 17x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-18 + 25x + 3x2 = 0 + -17x + 17x + 2x2 + -2x2
-18 + 25x + 3x2 = -17x + 17x + 2x2 + -2x2

Combine like terms: -17x + 17x = 0
-18 + 25x + 3x2 = 0 + 2x2 + -2x2
-18 + 25x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + 25x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -3x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-9, 0.6666666667}

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