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

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


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

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

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

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

Combine like terms: 2x + -9x = -7x
(-6 + -7x + 3x2) = 4

Solving
-6 + -7x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-6 + -4 + -7x + 3x2 = 4 + -4

Combine like terms: -6 + -4 = -10
-10 + -7x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-10 + -7x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(10 + -3x) = 0


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 '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {-1, 3.333333333}

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