4x(x-1)+15=x(3x+4)

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Solution for 4x(x-1)+15=x(3x+4) equation: 


Simplifying
4x(x + -1) + 15 = x(3x + 4)

Reorder the terms:
4x(-1 + x) + 15 = x(3x + 4)
(-1 * 4x + x * 4x) + 15 = x(3x + 4)
(-4x + 4x2) + 15 = x(3x + 4)

Reorder the terms:
15 + -4x + 4x2 = x(3x + 4)

Reorder the terms:
15 + -4x + 4x2 = x(4 + 3x)
15 + -4x + 4x2 = (4 * x + 3x * x)
15 + -4x + 4x2 = (4x + 3x2)

Solving
15 + -4x + 4x2 = 4x + 3x2

Solving for variable 'x'.

Reorder the terms:
15 + -4x + -4x + 4x2 + -3x2 = 4x + 3x2 + -4x + -3x2

Combine like terms: -4x + -4x = -8x
15 + -8x + 4x2 + -3x2 = 4x + 3x2 + -4x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
15 + -8x + 1x2 = 4x + 3x2 + -4x + -3x2

Reorder the terms:
15 + -8x + 1x2 = 4x + -4x + 3x2 + -3x2

Combine like terms: 4x + -4x = 0
15 + -8x + 1x2 = 0 + 3x2 + -3x2
15 + -8x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15 + -8x + 1x2 = 0

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, 5}

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