4x(x+3)=(3x)x+17x+84

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Solution for 4x(x+3)=(3x)x+17x+84 equation: 


Simplifying
4x(x + 3) = (3x) * x + 17x + 84

Reorder the terms:
4x(3 + x) = (3x) * x + 17x + 84
(3 * 4x + x * 4x) = (3x) * x + 17x + 84
(12x + 4x2) = (3x) * x + 17x + 84

Remove parenthesis around (3x)
12x + 4x2 = 3x * x + 17x + 84

Multiply x * x
12x + 4x2 = 3x2 + 17x + 84

Reorder the terms:
12x + 4x2 = 84 + 17x + 3x2

Solving
12x + 4x2 = 84 + 17x + 3x2

Solving for variable 'x'.

Reorder the terms:
-84 + 12x + -17x + 4x2 + -3x2 = 84 + 17x + 3x2 + -84 + -17x + -3x2

Combine like terms: 12x + -17x = -5x
-84 + -5x + 4x2 + -3x2 = 84 + 17x + 3x2 + -84 + -17x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-84 + -5x + 1x2 = 84 + 17x + 3x2 + -84 + -17x + -3x2

Reorder the terms:
-84 + -5x + 1x2 = 84 + -84 + 17x + -17x + 3x2 + -3x2

Combine like terms: 84 + -84 = 0
-84 + -5x + 1x2 = 0 + 17x + -17x + 3x2 + -3x2
-84 + -5x + 1x2 = 17x + -17x + 3x2 + -3x2

Combine like terms: 17x + -17x = 0
-84 + -5x + 1x2 = 0 + 3x2 + -3x2
-84 + -5x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-84 + -5x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-7, 12}

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