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

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


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

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

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

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

Combine like terms: -12x + 5x = -7x
(-20 + -7x + 3x2) = 4x

Solving
-20 + -7x + 3x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-20 + -7x + -4x + 3x2 = 4x + -4x

Combine like terms: -7x + -4x = -11x
-20 + -11x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + -11x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.333333333, 5}

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