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

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


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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

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


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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 3}

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