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

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

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

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

Multiply (3 + x) * (5 + -2x)
(3(5 + -2x) + x(5 + -2x)) = (x + 3)(7 + x)
((5 * 3 + -2x * 3) + x(5 + -2x)) = (x + 3)(7 + x)
((15 + -6x) + x(5 + -2x)) = (x + 3)(7 + x)
(15 + -6x + (5 * x + -2x * x)) = (x + 3)(7 + x)
(15 + -6x + (5x + -2x2)) = (x + 3)(7 + x)

Combine like terms: -6x + 5x = -1x
(15 + -1x + -2x2) = (x + 3)(7 + x)

Reorder the terms:
15 + -1x + -2x2 = (3 + x)(7 + x)

Multiply (3 + x) * (7 + x)
15 + -1x + -2x2 = (3(7 + x) + x(7 + x))
15 + -1x + -2x2 = ((7 * 3 + x * 3) + x(7 + x))
15 + -1x + -2x2 = ((21 + 3x) + x(7 + x))
15 + -1x + -2x2 = (21 + 3x + (7 * x + x * x))
15 + -1x + -2x2 = (21 + 3x + (7x + x2))

Combine like terms: 3x + 7x = 10x
15 + -1x + -2x2 = (21 + 10x + x2)

Solving
15 + -1x + -2x2 = 21 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
15 + -21 + -1x + -10x + -2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: 15 + -21 = -6
-6 + -1x + -10x + -2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: -1x + -10x = -11x
-6 + -11x + -2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: -2x2 + -1x2 = -3x2
-6 + -11x + -3x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Reorder the terms:
-6 + -11x + -3x2 = 21 + -21 + 10x + -10x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-6 + -11x + -3x2 = 0 + 10x + -10x + x2 + -1x2
-6 + -11x + -3x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-6 + -11x + -3x2 = 0 + x2 + -1x2
-6 + -11x + -3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11x + 3x2) = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-3, -0.6666666667}