x(6x-5)=3+2x

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Solution for x(6x-5)=3+2x equation:


Simplifying
x(6x + -5) = 3 + 2x

Reorder the terms:
x(-5 + 6x) = 3 + 2x
(-5 * x + 6x * x) = 3 + 2x
(-5x + 6x2) = 3 + 2x

Solving
-5x + 6x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + -5x + -2x + 6x2 = 3 + 2x + -3 + -2x

Combine like terms: -5x + -2x = -7x
-3 + -7x + 6x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-3 + -7x + 6x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-3 + -7x + 6x2 = 0 + 2x + -2x
-3 + -7x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + -7x + 6x2 = 0

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

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

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 = {-0.3333333333, 1.5}

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