(7-3x)(x+2)=4

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Solution for (7-3x)(x+2)=4 equation: 


Simplifying
(7 + -3x)(x + 2) = 4

Reorder the terms:
(7 + -3x)(2 + x) = 4

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

Combine like terms: 7x + -6x = 1x
(14 + 1x + -3x2) = 4

Solving
14 + 1x + -3x2 = 4

Solving for variable 'x'.

Reorder the terms:
14 + -4 + 1x + -3x2 = 4 + -4

Combine like terms: 14 + -4 = 10
10 + 1x + -3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
10 + 1x + -3x2 = 0

Factor a trinomial.
(2 + -1x)(5 + 3x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {2, -1.666666667}

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