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

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


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

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

Multiply (3 + -2x) * (5 + x)
(3(5 + x) + -2x * (5 + x)) = 7(x + 5)
((5 * 3 + x * 3) + -2x * (5 + x)) = 7(x + 5)
((15 + 3x) + -2x * (5 + x)) = 7(x + 5)
(15 + 3x + (5 * -2x + x * -2x)) = 7(x + 5)
(15 + 3x + (-10x + -2x2)) = 7(x + 5)

Combine like terms: 3x + -10x = -7x
(15 + -7x + -2x2) = 7(x + 5)

Reorder the terms:
15 + -7x + -2x2 = 7(5 + x)
15 + -7x + -2x2 = (5 * 7 + x * 7)
15 + -7x + -2x2 = (35 + 7x)

Solving
15 + -7x + -2x2 = 35 + 7x

Solving for variable 'x'.

Reorder the terms:
15 + -35 + -7x + -7x + -2x2 = 35 + 7x + -35 + -7x

Combine like terms: 15 + -35 = -20
-20 + -7x + -7x + -2x2 = 35 + 7x + -35 + -7x

Combine like terms: -7x + -7x = -14x
-20 + -14x + -2x2 = 35 + 7x + -35 + -7x

Reorder the terms:
-20 + -14x + -2x2 = 35 + -35 + 7x + -7x

Combine like terms: 35 + -35 = 0
-20 + -14x + -2x2 = 0 + 7x + -7x
-20 + -14x + -2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-20 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(10 + 7x + x2) = 0

Factor a trinomial.
-2((5 + x)(2 + x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-5, -2}

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