(2x-5)(3x-1)=-6(8x+2)+3

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Solution for (2x-5)(3x-1)=-6(8x+2)+3 equation: 


Simplifying
(2x + -5)(3x + -1) = -6(8x + 2) + 3

Reorder the terms:
(-5 + 2x)(3x + -1) = -6(8x + 2) + 3

Reorder the terms:
(-5 + 2x)(-1 + 3x) = -6(8x + 2) + 3

Multiply (-5 + 2x) * (-1 + 3x)
(-5(-1 + 3x) + 2x * (-1 + 3x)) = -6(8x + 2) + 3
((-1 * -5 + 3x * -5) + 2x * (-1 + 3x)) = -6(8x + 2) + 3
((5 + -15x) + 2x * (-1 + 3x)) = -6(8x + 2) + 3
(5 + -15x + (-1 * 2x + 3x * 2x)) = -6(8x + 2) + 3
(5 + -15x + (-2x + 6x2)) = -6(8x + 2) + 3

Combine like terms: -15x + -2x = -17x
(5 + -17x + 6x2) = -6(8x + 2) + 3

Reorder the terms:
5 + -17x + 6x2 = -6(2 + 8x) + 3
5 + -17x + 6x2 = (2 * -6 + 8x * -6) + 3
5 + -17x + 6x2 = (-12 + -48x) + 3

Reorder the terms:
5 + -17x + 6x2 = -12 + 3 + -48x

Combine like terms: -12 + 3 = -9
5 + -17x + 6x2 = -9 + -48x

Solving
5 + -17x + 6x2 = -9 + -48x

Solving for variable 'x'.

Reorder the terms:
5 + 9 + -17x + 48x + 6x2 = -9 + -48x + 9 + 48x

Combine like terms: 5 + 9 = 14
14 + -17x + 48x + 6x2 = -9 + -48x + 9 + 48x

Combine like terms: -17x + 48x = 31x
14 + 31x + 6x2 = -9 + -48x + 9 + 48x

Reorder the terms:
14 + 31x + 6x2 = -9 + 9 + -48x + 48x

Combine like terms: -9 + 9 = 0
14 + 31x + 6x2 = 0 + -48x + 48x
14 + 31x + 6x2 = -48x + 48x

Combine like terms: -48x + 48x = 0
14 + 31x + 6x2 = 0

Factor a trinomial.
(14 + 3x)(1 + 2x) = 0


Subproblem 1
Set the factor '(14 + 3x)' equal to zero and attempt to solve:

Simplifying
14 + 3x = 0

Solving
14 + 3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + 3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3x = 0 + -14
3x = 0 + -14

Combine like terms: 0 + -14 = -14
3x = -14

Divide each side by '3'.
x = -4.666666667

Simplifying
x = -4.666666667

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

Simplifying
1 + 2x = 0

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-4.666666667, -0.5}

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