(3x+5)(x-4)=12x-20

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Solution for (3x+5)(x-4)=12x-20 equation: 


Simplifying
(3x + 5)(x + -4) = 12x + -20

Reorder the terms:
(5 + 3x)(x + -4) = 12x + -20

Reorder the terms:
(5 + 3x)(-4 + x) = 12x + -20

Multiply (5 + 3x) * (-4 + x)
(5(-4 + x) + 3x * (-4 + x)) = 12x + -20
((-4 * 5 + x * 5) + 3x * (-4 + x)) = 12x + -20
((-20 + 5x) + 3x * (-4 + x)) = 12x + -20
(-20 + 5x + (-4 * 3x + x * 3x)) = 12x + -20
(-20 + 5x + (-12x + 3x2)) = 12x + -20

Combine like terms: 5x + -12x = -7x
(-20 + -7x + 3x2) = 12x + -20

Reorder the terms:
-20 + -7x + 3x2 = -20 + 12x

Add '20' to each side of the equation.
-20 + -7x + 20 + 3x2 = -20 + 20 + 12x

Reorder the terms:
-20 + 20 + -7x + 3x2 = -20 + 20 + 12x

Combine like terms: -20 + 20 = 0
0 + -7x + 3x2 = -20 + 20 + 12x
-7x + 3x2 = -20 + 20 + 12x

Combine like terms: -20 + 20 = 0
-7x + 3x2 = 0 + 12x
-7x + 3x2 = 12x

Solving
-7x + 3x2 = 12x

Solving for variable 'x'.

Reorder the terms:
-7x + -12x + 3x2 = 12x + -12x

Combine like terms: -7x + -12x = -19x
-19x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-19x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-19 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-19 + 3x)' equal to zero and attempt to solve:

Simplifying
-19 + 3x = 0

Solving
-19 + 3x = 0

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

Add '19' to each side of the equation.
-19 + 19 + 3x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 3x = 0 + 19
3x = 0 + 19

Combine like terms: 0 + 19 = 19
3x = 19

Divide each side by '3'.
x = 6.333333333

Simplifying
x = 6.333333333
Solution
x = {0, 6.333333333}

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