(3x-2)(x+7)=(x+10)(2x-1)

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Solution for (3x-2)(x+7)=(x+10)(2x-1) equation: 


Simplifying
(3x + -2)(x + 7) = (x + 10)(2x + -1)

Reorder the terms:
(-2 + 3x)(x + 7) = (x + 10)(2x + -1)

Reorder the terms:
(-2 + 3x)(7 + x) = (x + 10)(2x + -1)

Multiply (-2 + 3x) * (7 + x)
(-2(7 + x) + 3x * (7 + x)) = (x + 10)(2x + -1)
((7 * -2 + x * -2) + 3x * (7 + x)) = (x + 10)(2x + -1)
((-14 + -2x) + 3x * (7 + x)) = (x + 10)(2x + -1)
(-14 + -2x + (7 * 3x + x * 3x)) = (x + 10)(2x + -1)
(-14 + -2x + (21x + 3x2)) = (x + 10)(2x + -1)

Combine like terms: -2x + 21x = 19x
(-14 + 19x + 3x2) = (x + 10)(2x + -1)

Reorder the terms:
-14 + 19x + 3x2 = (10 + x)(2x + -1)

Reorder the terms:
-14 + 19x + 3x2 = (10 + x)(-1 + 2x)

Multiply (10 + x) * (-1 + 2x)
-14 + 19x + 3x2 = (10(-1 + 2x) + x(-1 + 2x))
-14 + 19x + 3x2 = ((-1 * 10 + 2x * 10) + x(-1 + 2x))
-14 + 19x + 3x2 = ((-10 + 20x) + x(-1 + 2x))
-14 + 19x + 3x2 = (-10 + 20x + (-1 * x + 2x * x))
-14 + 19x + 3x2 = (-10 + 20x + (-1x + 2x2))

Combine like terms: 20x + -1x = 19x
-14 + 19x + 3x2 = (-10 + 19x + 2x2)

Add '-19x' to each side of the equation.
-14 + 19x + -19x + 3x2 = -10 + 19x + -19x + 2x2

Combine like terms: 19x + -19x = 0
-14 + 0 + 3x2 = -10 + 19x + -19x + 2x2
-14 + 3x2 = -10 + 19x + -19x + 2x2

Combine like terms: 19x + -19x = 0
-14 + 3x2 = -10 + 0 + 2x2
-14 + 3x2 = -10 + 2x2

Solving
-14 + 3x2 = -10 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
-14 + 3x2 + -2x2 = -10 + 2x2 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-14 + 1x2 = -10 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-14 + 1x2 = -10 + 0
-14 + 1x2 = -10

Add '14' to each side of the equation.
-14 + 14 + 1x2 = -10 + 14

Combine like terms: -14 + 14 = 0
0 + 1x2 = -10 + 14
1x2 = -10 + 14

Combine like terms: -10 + 14 = 4
1x2 = 4

Divide each side by '1'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}

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