(x+7)(2-3x)=(x+7)(18-x)

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Solution for (x+7)(2-3x)=(x+7)(18-x) equation: 


Simplifying
(x + 7)(2 + -3x) = (x + 7)(18 + -1x)

Reorder the terms:
(7 + x)(2 + -3x) = (x + 7)(18 + -1x)

Multiply (7 + x) * (2 + -3x)
(7(2 + -3x) + x(2 + -3x)) = (x + 7)(18 + -1x)
((2 * 7 + -3x * 7) + x(2 + -3x)) = (x + 7)(18 + -1x)
((14 + -21x) + x(2 + -3x)) = (x + 7)(18 + -1x)
(14 + -21x + (2 * x + -3x * x)) = (x + 7)(18 + -1x)
(14 + -21x + (2x + -3x2)) = (x + 7)(18 + -1x)

Combine like terms: -21x + 2x = -19x
(14 + -19x + -3x2) = (x + 7)(18 + -1x)

Reorder the terms:
14 + -19x + -3x2 = (7 + x)(18 + -1x)

Multiply (7 + x) * (18 + -1x)
14 + -19x + -3x2 = (7(18 + -1x) + x(18 + -1x))
14 + -19x + -3x2 = ((18 * 7 + -1x * 7) + x(18 + -1x))
14 + -19x + -3x2 = ((126 + -7x) + x(18 + -1x))
14 + -19x + -3x2 = (126 + -7x + (18 * x + -1x * x))
14 + -19x + -3x2 = (126 + -7x + (18x + -1x2))

Combine like terms: -7x + 18x = 11x
14 + -19x + -3x2 = (126 + 11x + -1x2)

Solving
14 + -19x + -3x2 = 126 + 11x + -1x2

Solving for variable 'x'.

Reorder the terms:
14 + -126 + -19x + -11x + -3x2 + x2 = 126 + 11x + -1x2 + -126 + -11x + x2

Combine like terms: 14 + -126 = -112
-112 + -19x + -11x + -3x2 + x2 = 126 + 11x + -1x2 + -126 + -11x + x2

Combine like terms: -19x + -11x = -30x
-112 + -30x + -3x2 + x2 = 126 + 11x + -1x2 + -126 + -11x + x2

Combine like terms: -3x2 + x2 = -2x2
-112 + -30x + -2x2 = 126 + 11x + -1x2 + -126 + -11x + x2

Reorder the terms:
-112 + -30x + -2x2 = 126 + -126 + 11x + -11x + -1x2 + x2

Combine like terms: 126 + -126 = 0
-112 + -30x + -2x2 = 0 + 11x + -11x + -1x2 + x2
-112 + -30x + -2x2 = 11x + -11x + -1x2 + x2

Combine like terms: 11x + -11x = 0
-112 + -30x + -2x2 = 0 + -1x2 + x2
-112 + -30x + -2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-112 + -30x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(56 + 15x + x2) = 0

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

Ignore the factor -2.

Subproblem 1
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

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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Solution
x = {-8, -7}

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