(3x+7)(x-5)=6x+14

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Solution for (3x+7)(x-5)=6x+14 equation: 


Simplifying
(3x + 7)(x + -5) = 6x + 14

Reorder the terms:
(7 + 3x)(x + -5) = 6x + 14

Reorder the terms:
(7 + 3x)(-5 + x) = 6x + 14

Multiply (7 + 3x) * (-5 + x)
(7(-5 + x) + 3x * (-5 + x)) = 6x + 14
((-5 * 7 + x * 7) + 3x * (-5 + x)) = 6x + 14
((-35 + 7x) + 3x * (-5 + x)) = 6x + 14
(-35 + 7x + (-5 * 3x + x * 3x)) = 6x + 14
(-35 + 7x + (-15x + 3x2)) = 6x + 14

Combine like terms: 7x + -15x = -8x
(-35 + -8x + 3x2) = 6x + 14

Reorder the terms:
-35 + -8x + 3x2 = 14 + 6x

Solving
-35 + -8x + 3x2 = 14 + 6x

Solving for variable 'x'.

Reorder the terms:
-35 + -14 + -8x + -6x + 3x2 = 14 + 6x + -14 + -6x

Combine like terms: -35 + -14 = -49
-49 + -8x + -6x + 3x2 = 14 + 6x + -14 + -6x

Combine like terms: -8x + -6x = -14x
-49 + -14x + 3x2 = 14 + 6x + -14 + -6x

Reorder the terms:
-49 + -14x + 3x2 = 14 + -14 + 6x + -6x

Combine like terms: 14 + -14 = 0
-49 + -14x + 3x2 = 0 + 6x + -6x
-49 + -14x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-49 + -14x + 3x2 = 0

Factor a trinomial.
(-7 + -3x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2.333333333, 7}

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