(2x+7)(x-6)-(4x+14)=0

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Solution for (2x+7)(x-6)-(4x+14)=0 equation: 


Simplifying
(2x + 7)(x + -6) + -1(4x + 14) = 0

Reorder the terms:
(7 + 2x)(x + -6) + -1(4x + 14) = 0

Reorder the terms:
(7 + 2x)(-6 + x) + -1(4x + 14) = 0

Multiply (7 + 2x) * (-6 + x)
(7(-6 + x) + 2x * (-6 + x)) + -1(4x + 14) = 0
((-6 * 7 + x * 7) + 2x * (-6 + x)) + -1(4x + 14) = 0
((-42 + 7x) + 2x * (-6 + x)) + -1(4x + 14) = 0
(-42 + 7x + (-6 * 2x + x * 2x)) + -1(4x + 14) = 0
(-42 + 7x + (-12x + 2x2)) + -1(4x + 14) = 0

Combine like terms: 7x + -12x = -5x
(-42 + -5x + 2x2) + -1(4x + 14) = 0

Reorder the terms:
-42 + -5x + 2x2 + -1(14 + 4x) = 0
-42 + -5x + 2x2 + (14 * -1 + 4x * -1) = 0
-42 + -5x + 2x2 + (-14 + -4x) = 0

Reorder the terms:
-42 + -14 + -5x + -4x + 2x2 = 0

Combine like terms: -42 + -14 = -56
-56 + -5x + -4x + 2x2 = 0

Combine like terms: -5x + -4x = -9x
-56 + -9x + 2x2 = 0

Solving
-56 + -9x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(8 + -1x) = 0


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

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3.5, 8}

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