7x(x-1)=12(x+3)

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Solution for 7x(x-1)=12(x+3) equation: 


Simplifying
7x(x + -1) = 12(x + 3)

Reorder the terms:
7x(-1 + x) = 12(x + 3)
(-1 * 7x + x * 7x) = 12(x + 3)
(-7x + 7x2) = 12(x + 3)

Reorder the terms:
-7x + 7x2 = 12(3 + x)
-7x + 7x2 = (3 * 12 + x * 12)
-7x + 7x2 = (36 + 12x)

Solving
-7x + 7x2 = 36 + 12x

Solving for variable 'x'.

Reorder the terms:
-36 + -7x + -12x + 7x2 = 36 + 12x + -36 + -12x

Combine like terms: -7x + -12x = -19x
-36 + -19x + 7x2 = 36 + 12x + -36 + -12x

Reorder the terms:
-36 + -19x + 7x2 = 36 + -36 + 12x + -12x

Combine like terms: 36 + -36 = 0
-36 + -19x + 7x2 = 0 + 12x + -12x
-36 + -19x + 7x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-36 + -19x + 7x2 = 0

Factor a trinomial.
(-9 + -7x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -7x)' equal to zero and attempt to solve:

Simplifying
-9 + -7x = 0

Solving
-9 + -7x = 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 + -7x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7x = 0 + 9
-7x = 0 + 9

Combine like terms: 0 + 9 = 9
-7x = 9

Divide each side by '-7'.
x = -1.285714286

Simplifying
x = -1.285714286

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 = {-1.285714286, 4}

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