7-3(x-5)(x+4)=21+20x

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Solution for 7-3(x-5)(x+4)=21+20x equation: 


Simplifying
7 + -3(x + -5)(x + 4) = 21 + 20x

Reorder the terms:
7 + -3(-5 + x)(x + 4) = 21 + 20x

Reorder the terms:
7 + -3(-5 + x)(4 + x) = 21 + 20x

Multiply (-5 + x) * (4 + x)
7 + -3(-5(4 + x) + x(4 + x)) = 21 + 20x
7 + -3((4 * -5 + x * -5) + x(4 + x)) = 21 + 20x
7 + -3((-20 + -5x) + x(4 + x)) = 21 + 20x
7 + -3(-20 + -5x + (4 * x + x * x)) = 21 + 20x
7 + -3(-20 + -5x + (4x + x2)) = 21 + 20x

Combine like terms: -5x + 4x = -1x
7 + -3(-20 + -1x + x2) = 21 + 20x
7 + (-20 * -3 + -1x * -3 + x2 * -3) = 21 + 20x
7 + (60 + 3x + -3x2) = 21 + 20x

Combine like terms: 7 + 60 = 67
67 + 3x + -3x2 = 21 + 20x

Solving
67 + 3x + -3x2 = 21 + 20x

Solving for variable 'x'.

Reorder the terms:
67 + -21 + 3x + -20x + -3x2 = 21 + 20x + -21 + -20x

Combine like terms: 67 + -21 = 46
46 + 3x + -20x + -3x2 = 21 + 20x + -21 + -20x

Combine like terms: 3x + -20x = -17x
46 + -17x + -3x2 = 21 + 20x + -21 + -20x

Reorder the terms:
46 + -17x + -3x2 = 21 + -21 + 20x + -20x

Combine like terms: 21 + -21 = 0
46 + -17x + -3x2 = 0 + 20x + -20x
46 + -17x + -3x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
46 + -17x + -3x2 = 0

Factor a trinomial.
(2 + -1x)(23 + 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 '(23 + 3x)' equal to zero and attempt to solve:

Simplifying
23 + 3x = 0

Solving
23 + 3x = 0

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

Add '-23' to each side of the equation.
23 + -23 + 3x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 3x = 0 + -23
3x = 0 + -23

Combine like terms: 0 + -23 = -23
3x = -23

Divide each side by '3'.
x = -7.666666667

Simplifying
x = -7.666666667
Solution
x = {2, -7.666666667}

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