6x^2-15x+2=2x^2+10x-4

Solution for 6x^2-15x+2=2x^2+10x-4 equation:

Simplifying
6x2 + -15x + 2 = 2x2 + 10x + -4

Reorder the terms:
2 + -15x + 6x2 = 2x2 + 10x + -4

Reorder the terms:
2 + -15x + 6x2 = -4 + 10x + 2x2

Solving
2 + -15x + 6x2 = -4 + 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + 4 + -15x + -10x + 6x2 + -2x2 = -4 + 10x + 2x2 + 4 + -10x + -2x2

Combine like terms: 2 + 4 = 6
6 + -15x + -10x + 6x2 + -2x2 = -4 + 10x + 2x2 + 4 + -10x + -2x2

Combine like terms: -15x + -10x = -25x
6 + -25x + 6x2 + -2x2 = -4 + 10x + 2x2 + 4 + -10x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
6 + -25x + 4x2 = -4 + 10x + 2x2 + 4 + -10x + -2x2

Reorder the terms:
6 + -25x + 4x2 = -4 + 4 + 10x + -10x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
6 + -25x + 4x2 = 0 + 10x + -10x + 2x2 + -2x2
6 + -25x + 4x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
6 + -25x + 4x2 = 0 + 2x2 + -2x2
6 + -25x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -25x + 4x2 = 0

Factor a trinomial.
(1 + -4x)(6 + -1x) = 0

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.25, 6}