x(6x-7)=3x^2+3x-8

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Solution for x(6x-7)=3x^2+3x-8 equation: 


Simplifying
x(6x + -7) = 3x2 + 3x + -8

Reorder the terms:
x(-7 + 6x) = 3x2 + 3x + -8
(-7 * x + 6x * x) = 3x2 + 3x + -8
(-7x + 6x2) = 3x2 + 3x + -8

Reorder the terms:
-7x + 6x2 = -8 + 3x + 3x2

Solving
-7x + 6x2 = -8 + 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
8 + -7x + -3x + 6x2 + -3x2 = -8 + 3x + 3x2 + 8 + -3x + -3x2

Combine like terms: -7x + -3x = -10x
8 + -10x + 6x2 + -3x2 = -8 + 3x + 3x2 + 8 + -3x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
8 + -10x + 3x2 = -8 + 3x + 3x2 + 8 + -3x + -3x2

Reorder the terms:
8 + -10x + 3x2 = -8 + 8 + 3x + -3x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
8 + -10x + 3x2 = 0 + 3x + -3x + 3x2 + -3x2
8 + -10x + 3x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
8 + -10x + 3x2 = 0 + 3x2 + -3x2
8 + -10x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + -10x + 3x2 = 0

Factor a trinomial.
(4 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.333333333, 2}

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