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

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


Simplifying
(6x + -7)(x + -2) = (7x + 6)(x + -3)

Reorder the terms:
(-7 + 6x)(x + -2) = (7x + 6)(x + -3)

Reorder the terms:
(-7 + 6x)(-2 + x) = (7x + 6)(x + -3)

Multiply (-7 + 6x) * (-2 + x)
(-7(-2 + x) + 6x * (-2 + x)) = (7x + 6)(x + -3)
((-2 * -7 + x * -7) + 6x * (-2 + x)) = (7x + 6)(x + -3)
((14 + -7x) + 6x * (-2 + x)) = (7x + 6)(x + -3)
(14 + -7x + (-2 * 6x + x * 6x)) = (7x + 6)(x + -3)
(14 + -7x + (-12x + 6x2)) = (7x + 6)(x + -3)

Combine like terms: -7x + -12x = -19x
(14 + -19x + 6x2) = (7x + 6)(x + -3)

Reorder the terms:
14 + -19x + 6x2 = (6 + 7x)(x + -3)

Reorder the terms:
14 + -19x + 6x2 = (6 + 7x)(-3 + x)

Multiply (6 + 7x) * (-3 + x)
14 + -19x + 6x2 = (6(-3 + x) + 7x * (-3 + x))
14 + -19x + 6x2 = ((-3 * 6 + x * 6) + 7x * (-3 + x))
14 + -19x + 6x2 = ((-18 + 6x) + 7x * (-3 + x))
14 + -19x + 6x2 = (-18 + 6x + (-3 * 7x + x * 7x))
14 + -19x + 6x2 = (-18 + 6x + (-21x + 7x2))

Combine like terms: 6x + -21x = -15x
14 + -19x + 6x2 = (-18 + -15x + 7x2)

Solving
14 + -19x + 6x2 = -18 + -15x + 7x2

Solving for variable 'x'.

Reorder the terms:
14 + 18 + -19x + 15x + 6x2 + -7x2 = -18 + -15x + 7x2 + 18 + 15x + -7x2

Combine like terms: 14 + 18 = 32
32 + -19x + 15x + 6x2 + -7x2 = -18 + -15x + 7x2 + 18 + 15x + -7x2

Combine like terms: -19x + 15x = -4x
32 + -4x + 6x2 + -7x2 = -18 + -15x + 7x2 + 18 + 15x + -7x2

Combine like terms: 6x2 + -7x2 = -1x2
32 + -4x + -1x2 = -18 + -15x + 7x2 + 18 + 15x + -7x2

Reorder the terms:
32 + -4x + -1x2 = -18 + 18 + -15x + 15x + 7x2 + -7x2

Combine like terms: -18 + 18 = 0
32 + -4x + -1x2 = 0 + -15x + 15x + 7x2 + -7x2
32 + -4x + -1x2 = -15x + 15x + 7x2 + -7x2

Combine like terms: -15x + 15x = 0
32 + -4x + -1x2 = 0 + 7x2 + -7x2
32 + -4x + -1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
32 + -4x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(8 + x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

Simplifying
x = -8
Solution
x = {4, -8}

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