(x-3)(3x+4)=10

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Solution for (x-3)(3x+4)=10 equation: 


Simplifying
(x + -3)(3x + 4) = 10

Reorder the terms:
(-3 + x)(3x + 4) = 10

Reorder the terms:
(-3 + x)(4 + 3x) = 10

Multiply (-3 + x) * (4 + 3x)
(-3(4 + 3x) + x(4 + 3x)) = 10
((4 * -3 + 3x * -3) + x(4 + 3x)) = 10
((-12 + -9x) + x(4 + 3x)) = 10
(-12 + -9x + (4 * x + 3x * x)) = 10
(-12 + -9x + (4x + 3x2)) = 10

Combine like terms: -9x + 4x = -5x
(-12 + -5x + 3x2) = 10

Solving
-12 + -5x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-12 + -10 + -5x + 3x2 = 10 + -10

Combine like terms: -12 + -10 = -22
-22 + -5x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-22 + -5x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -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 '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {-2, 3.666666667}

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