(2x+7)(3-2x)=9

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Solution for (2x+7)(3-2x)=9 equation: 


Simplifying
(2x + 7)(3 + -2x) = 9

Reorder the terms:
(7 + 2x)(3 + -2x) = 9

Multiply (7 + 2x) * (3 + -2x)
(7(3 + -2x) + 2x * (3 + -2x)) = 9
((3 * 7 + -2x * 7) + 2x * (3 + -2x)) = 9
((21 + -14x) + 2x * (3 + -2x)) = 9
(21 + -14x + (3 * 2x + -2x * 2x)) = 9
(21 + -14x + (6x + -4x2)) = 9

Combine like terms: -14x + 6x = -8x
(21 + -8x + -4x2) = 9

Solving
21 + -8x + -4x2 = 9

Solving for variable 'x'.

Reorder the terms:
21 + -9 + -8x + -4x2 = 9 + -9

Combine like terms: 21 + -9 = 12
12 + -8x + -4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
12 + -8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -2x + -1x2) = 0

Factor a trinomial.
4((1 + -1x)(3 + x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -3}

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