12x(x+1)=42(x+1)-(3x-42)

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Solution for 12x(x+1)=42(x+1)-(3x-42) equation: 


Simplifying
12x(x + 1) = 42(x + 1) + -1(3x + -42)

Reorder the terms:
12x(1 + x) = 42(x + 1) + -1(3x + -42)
(1 * 12x + x * 12x) = 42(x + 1) + -1(3x + -42)
(12x + 12x2) = 42(x + 1) + -1(3x + -42)

Reorder the terms:
12x + 12x2 = 42(1 + x) + -1(3x + -42)
12x + 12x2 = (1 * 42 + x * 42) + -1(3x + -42)
12x + 12x2 = (42 + 42x) + -1(3x + -42)

Reorder the terms:
12x + 12x2 = 42 + 42x + -1(-42 + 3x)
12x + 12x2 = 42 + 42x + (-42 * -1 + 3x * -1)
12x + 12x2 = 42 + 42x + (42 + -3x)

Reorder the terms:
12x + 12x2 = 42 + 42 + 42x + -3x

Combine like terms: 42 + 42 = 84
12x + 12x2 = 84 + 42x + -3x

Combine like terms: 42x + -3x = 39x
12x + 12x2 = 84 + 39x

Solving
12x + 12x2 = 84 + 39x

Solving for variable 'x'.

Reorder the terms:
-84 + 12x + -39x + 12x2 = 84 + 39x + -84 + -39x

Combine like terms: 12x + -39x = -27x
-84 + -27x + 12x2 = 84 + 39x + -84 + -39x

Reorder the terms:
-84 + -27x + 12x2 = 84 + -84 + 39x + -39x

Combine like terms: 84 + -84 = 0
-84 + -27x + 12x2 = 0 + 39x + -39x
-84 + -27x + 12x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
-84 + -27x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -9x + 4x2) = 0

Factor a trinomial.
3((-7 + -4x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.75, 4}

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