4x^2+5x+21=3x^2+21x-42

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Solution for 4x^2+5x+21=3x^2+21x-42 equation: 


Simplifying
4x2 + 5x + 21 = 3x2 + 21x + -42

Reorder the terms:
21 + 5x + 4x2 = 3x2 + 21x + -42

Reorder the terms:
21 + 5x + 4x2 = -42 + 21x + 3x2

Solving
21 + 5x + 4x2 = -42 + 21x + 3x2

Solving for variable 'x'.

Reorder the terms:
21 + 42 + 5x + -21x + 4x2 + -3x2 = -42 + 21x + 3x2 + 42 + -21x + -3x2

Combine like terms: 21 + 42 = 63
63 + 5x + -21x + 4x2 + -3x2 = -42 + 21x + 3x2 + 42 + -21x + -3x2

Combine like terms: 5x + -21x = -16x
63 + -16x + 4x2 + -3x2 = -42 + 21x + 3x2 + 42 + -21x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
63 + -16x + 1x2 = -42 + 21x + 3x2 + 42 + -21x + -3x2

Reorder the terms:
63 + -16x + 1x2 = -42 + 42 + 21x + -21x + 3x2 + -3x2

Combine like terms: -42 + 42 = 0
63 + -16x + 1x2 = 0 + 21x + -21x + 3x2 + -3x2
63 + -16x + 1x2 = 21x + -21x + 3x2 + -3x2

Combine like terms: 21x + -21x = 0
63 + -16x + 1x2 = 0 + 3x2 + -3x2
63 + -16x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
63 + -16x + 1x2 = 0

Factor a trinomial.
(7 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {7, 9}

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