4x(x+1)=15

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

Simplifying
4x(x + 1) = 15

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

Solving
4x + 4x2 = 15

Solving for variable 'x'.

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

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

Factor a trinomial.
(-5 + -2x)(3 + -2x) = 0

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2.5, 1.5}