10x^2=39x-27

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Solution for 10x^2=39x-27 equation:


Simplifying
10x2 = 39x + -27

Reorder the terms:
10x2 = -27 + 39x

Solving
10x2 = -27 + 39x

Solving for variable 'x'.

Reorder the terms:
27 + -39x + 10x2 = -27 + 39x + 27 + -39x

Reorder the terms:
27 + -39x + 10x2 = -27 + 27 + 39x + -39x

Combine like terms: -27 + 27 = 0
27 + -39x + 10x2 = 0 + 39x + -39x
27 + -39x + 10x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
27 + -39x + 10x2 = 0

Factor a trinomial.
(9 + -10x)(3 + -1x) = 0

Subproblem 1

Set the factor '(9 + -10x)' equal to zero and attempt to solve: Simplifying 9 + -10x = 0 Solving 9 + -10x = 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 + -10x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10x = 0 + -9 -10x = 0 + -9 Combine like terms: 0 + -9 = -9 -10x = -9 Divide each side by '-10'. x = 0.9 Simplifying x = 0.9

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 = {0.9, 3}

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