2x(5x+6)=2+4(2x+1)

Solution for 2x(5x+6)=2+4(2x+1) equation:

Simplifying
2x(5x + 6) = 2 + 4(2x + 1)

Reorder the terms:
2x(6 + 5x) = 2 + 4(2x + 1)
(6 * 2x + 5x * 2x) = 2 + 4(2x + 1)
(12x + 10x2) = 2 + 4(2x + 1)

Reorder the terms:
12x + 10x2 = 2 + 4(1 + 2x)
12x + 10x2 = 2 + (1 * 4 + 2x * 4)
12x + 10x2 = 2 + (4 + 8x)

Combine like terms: 2 + 4 = 6
12x + 10x2 = 6 + 8x

Solving
12x + 10x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + -8x + 10x2 = 6 + 8x + -6 + -8x

Combine like terms: 12x + -8x = 4x
-6 + 4x + 10x2 = 6 + 8x + -6 + -8x

Reorder the terms:
-6 + 4x + 10x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
-6 + 4x + 10x2 = 0 + 8x + -8x
-6 + 4x + 10x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-6 + 4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2x + 5x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -5x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-1, 0.6}