What is the answer to roots 6a^2x+4ab+2a-3abx-2b^2-b ?

The answer to roots 6a^2x+4ab+2a-3abx-2b^2-b is x=-(2b+1)/(3a);\quad a\ne 0,a\ne b/2

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roots 6a^2x+4ab+2a-3abx-2b^2-b

roots

6 a^{2} x + 4 ab + 2 a - 3 ab x - 2 b^{2} - b

x = - \frac{2 b + 1}{3 a}; a \neq = 0, a \neq = \frac{b}{2}

Solution steps

6 a^{2} x + 4 ab + 2 a - 3 ab x - 2 b^{2} - b

The roots are the intercepts with the x-axis

(y = 0)

6 a^{2} x + 4 ab + 2 a - 3 ab x - 2 b^{2} - b = 0

Move

4 ab

to the right side

6 a^{2} x + 2 a - 3 ab x - 2 b^{2} - b = - 4 ab

Move

2 a

to the right side

6 a^{2} x - 3 ab x - 2 b^{2} - b = - 4 ab - 2 a

Move

2 b^{2}

to the right side

6 a^{2} x - 3 ab x - b = - 4 ab - 2 a + 2 b^{2}

Move

b

to the right side

6 a^{2} x - 3 ab x = - 4 ab - 2 a + 2 b^{2} + b

Factor

6 a^{2} x - 3 ab x : 3 a x (2 a - b)

3 a x (2 a - b) = - 4 ab - 2 a + 2 b^{2} + b

Divide both sides by

3 a (2 a - b); a \neq = 0, a \neq = \frac{b}{2}

x = - \frac{2 b + 1}{3 a}; a \neq = 0, a \neq = \frac{b}{2}

7 x + 11 = 4 x + 2

w, 350 - 4 w = - 10 + 6 w

5 = 31 (2 x + 12)

a, z = a + \frac{b}{c}

x, y = 20 v - 36 x + 10 y

What is the answer to roots 6a^2x+4ab+2a-3abx-2b^2-b ?
The answer to roots 6a^2x+4ab+2a-3abx-2b^2-b is x=-(2b+1)/(3a);\quad a\ne 0,a\ne b/2