(x+4)*(2x-3)=21

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Solution for (x+4)*(2x-3)=21 equation: 


Simplifying
(x + 4)(2x + -3) = 21

Reorder the terms:
(4 + x)(2x + -3) = 21

Reorder the terms:
(4 + x)(-3 + 2x) = 21

Multiply (4 + x) * (-3 + 2x)
(4(-3 + 2x) + x(-3 + 2x)) = 21
((-3 * 4 + 2x * 4) + x(-3 + 2x)) = 21
((-12 + 8x) + x(-3 + 2x)) = 21
(-12 + 8x + (-3 * x + 2x * x)) = 21
(-12 + 8x + (-3x + 2x2)) = 21

Combine like terms: 8x + -3x = 5x
(-12 + 5x + 2x2) = 21

Solving
-12 + 5x + 2x2 = 21

Solving for variable 'x'.

Reorder the terms:
-12 + -21 + 5x + 2x2 = 21 + -21

Combine like terms: -12 + -21 = -33
-33 + 5x + 2x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-33 + 5x + 2x2 = 0

Factor a trinomial.
(-11 + -2x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve:

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 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 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5.5, 3}

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