4x^2+6=2x^2+3(5x+2)

Solution for 4x^2+6=2x^2+3(5x+2) equation:

Simplifying
4x2 + 6 = 2x2 + 3(5x + 2)

Reorder the terms:
6 + 4x2 = 2x2 + 3(5x + 2)

Reorder the terms:
6 + 4x2 = 2x2 + 3(2 + 5x)
6 + 4x2 = 2x2 + (2 * 3 + 5x * 3)
6 + 4x2 = 2x2 + (6 + 15x)

Reorder the terms:
6 + 4x2 = 6 + 15x + 2x2

Add '-6' to each side of the equation.
6 + -6 + 4x2 = 6 + 15x + -6 + 2x2

Combine like terms: 6 + -6 = 0
0 + 4x2 = 6 + 15x + -6 + 2x2
4x2 = 6 + 15x + -6 + 2x2

Reorder the terms:
4x2 = 6 + -6 + 15x + 2x2

Combine like terms: 6 + -6 = 0
4x2 = 0 + 15x + 2x2
4x2 = 15x + 2x2

Solving
4x2 = 15x + 2x2

Solving for variable 'x'.

Reorder the terms:
-15x + 4x2 + -2x2 = 15x + 2x2 + -15x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-15x + 2x2 = 15x + 2x2 + -15x + -2x2

Reorder the terms:
-15x + 2x2 = 15x + -15x + 2x2 + -2x2

Combine like terms: 15x + -15x = 0
-15x + 2x2 = 0 + 2x2 + -2x2
-15x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + 2x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-15 + 2x)' equal to zero and attempt to solve:

Simplifying
-15 + 2x = 0

Solving
-15 + 2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 0 + 15
2x = 0 + 15

Combine like terms: 0 + 15 = 15
2x = 15

Divide each side by '2'.
x = 7.5

Simplifying
x = 7.5
Solution
x = {0, 7.5}