(7-x)(2x+3)=(2x+3)(x-5)

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Solution for (7-x)(2x+3)=(2x+3)(x-5) equation: 


Simplifying
(7 + -1x)(2x + 3) = (2x + 3)(x + -5)

Reorder the terms:
(7 + -1x)(3 + 2x) = (2x + 3)(x + -5)

Multiply (7 + -1x) * (3 + 2x)
(7(3 + 2x) + -1x * (3 + 2x)) = (2x + 3)(x + -5)
((3 * 7 + 2x * 7) + -1x * (3 + 2x)) = (2x + 3)(x + -5)
((21 + 14x) + -1x * (3 + 2x)) = (2x + 3)(x + -5)
(21 + 14x + (3 * -1x + 2x * -1x)) = (2x + 3)(x + -5)
(21 + 14x + (-3x + -2x2)) = (2x + 3)(x + -5)

Combine like terms: 14x + -3x = 11x
(21 + 11x + -2x2) = (2x + 3)(x + -5)

Reorder the terms:
21 + 11x + -2x2 = (3 + 2x)(x + -5)

Reorder the terms:
21 + 11x + -2x2 = (3 + 2x)(-5 + x)

Multiply (3 + 2x) * (-5 + x)
21 + 11x + -2x2 = (3(-5 + x) + 2x * (-5 + x))
21 + 11x + -2x2 = ((-5 * 3 + x * 3) + 2x * (-5 + x))
21 + 11x + -2x2 = ((-15 + 3x) + 2x * (-5 + x))
21 + 11x + -2x2 = (-15 + 3x + (-5 * 2x + x * 2x))
21 + 11x + -2x2 = (-15 + 3x + (-10x + 2x2))

Combine like terms: 3x + -10x = -7x
21 + 11x + -2x2 = (-15 + -7x + 2x2)

Solving
21 + 11x + -2x2 = -15 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
21 + 15 + 11x + 7x + -2x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Combine like terms: 21 + 15 = 36
36 + 11x + 7x + -2x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Combine like terms: 11x + 7x = 18x
36 + 18x + -2x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Combine like terms: -2x2 + -2x2 = -4x2
36 + 18x + -4x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Reorder the terms:
36 + 18x + -4x2 = -15 + 15 + -7x + 7x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
36 + 18x + -4x2 = 0 + -7x + 7x + 2x2 + -2x2
36 + 18x + -4x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
36 + 18x + -4x2 = 0 + 2x2 + -2x2
36 + 18x + -4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
36 + 18x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 9x + -2x2) = 0

Factor a trinomial.
2((6 + -1x)(3 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {6, -1.5}

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