(3x-2)(2x+1)=(6x+5)(x-2)+7

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Solution for (3x-2)(2x+1)=(6x+5)(x-2)+7 equation: 


Simplifying
(3x + -2)(2x + 1) = (6x + 5)(x + -2) + 7

Reorder the terms:
(-2 + 3x)(2x + 1) = (6x + 5)(x + -2) + 7

Reorder the terms:
(-2 + 3x)(1 + 2x) = (6x + 5)(x + -2) + 7

Multiply (-2 + 3x) * (1 + 2x)
(-2(1 + 2x) + 3x * (1 + 2x)) = (6x + 5)(x + -2) + 7
((1 * -2 + 2x * -2) + 3x * (1 + 2x)) = (6x + 5)(x + -2) + 7
((-2 + -4x) + 3x * (1 + 2x)) = (6x + 5)(x + -2) + 7
(-2 + -4x + (1 * 3x + 2x * 3x)) = (6x + 5)(x + -2) + 7
(-2 + -4x + (3x + 6x2)) = (6x + 5)(x + -2) + 7

Combine like terms: -4x + 3x = -1x
(-2 + -1x + 6x2) = (6x + 5)(x + -2) + 7

Reorder the terms:
-2 + -1x + 6x2 = (5 + 6x)(x + -2) + 7

Reorder the terms:
-2 + -1x + 6x2 = (5 + 6x)(-2 + x) + 7

Multiply (5 + 6x) * (-2 + x)
-2 + -1x + 6x2 = (5(-2 + x) + 6x * (-2 + x)) + 7
-2 + -1x + 6x2 = ((-2 * 5 + x * 5) + 6x * (-2 + x)) + 7
-2 + -1x + 6x2 = ((-10 + 5x) + 6x * (-2 + x)) + 7
-2 + -1x + 6x2 = (-10 + 5x + (-2 * 6x + x * 6x)) + 7
-2 + -1x + 6x2 = (-10 + 5x + (-12x + 6x2)) + 7

Combine like terms: 5x + -12x = -7x
-2 + -1x + 6x2 = (-10 + -7x + 6x2) + 7

Reorder the terms:
-2 + -1x + 6x2 = -10 + 7 + -7x + 6x2

Combine like terms: -10 + 7 = -3
-2 + -1x + 6x2 = -3 + -7x + 6x2

Add '-6x2' to each side of the equation.
-2 + -1x + 6x2 + -6x2 = -3 + -7x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2 + -1x + 0 = -3 + -7x + 6x2 + -6x2
-2 + -1x = -3 + -7x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2 + -1x = -3 + -7x + 0
-2 + -1x = -3 + -7x

Solving
-2 + -1x = -3 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
-2 + -1x + 7x = -3 + -7x + 7x

Combine like terms: -1x + 7x = 6x
-2 + 6x = -3 + -7x + 7x

Combine like terms: -7x + 7x = 0
-2 + 6x = -3 + 0
-2 + 6x = -3

Add '2' to each side of the equation.
-2 + 2 + 6x = -3 + 2

Combine like terms: -2 + 2 = 0
0 + 6x = -3 + 2
6x = -3 + 2

Combine like terms: -3 + 2 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

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