(3x-5)(2x+7)=(3x+1)(2x-3)+4x

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Solution for (3x-5)(2x+7)=(3x+1)(2x-3)+4x equation:


Simplifying
(3x + -5)(2x + 7) = (3x + 1)(2x + -3) + 4x

Reorder the terms:
(-5 + 3x)(2x + 7) = (3x + 1)(2x + -3) + 4x

Reorder the terms:
(-5 + 3x)(7 + 2x) = (3x + 1)(2x + -3) + 4x

Multiply (-5 + 3x) * (7 + 2x)
(-5(7 + 2x) + 3x * (7 + 2x)) = (3x + 1)(2x + -3) + 4x
((7 * -5 + 2x * -5) + 3x * (7 + 2x)) = (3x + 1)(2x + -3) + 4x
((-35 + -10x) + 3x * (7 + 2x)) = (3x + 1)(2x + -3) + 4x
(-35 + -10x + (7 * 3x + 2x * 3x)) = (3x + 1)(2x + -3) + 4x
(-35 + -10x + (21x + 6x2)) = (3x + 1)(2x + -3) + 4x

Combine like terms: -10x + 21x = 11x
(-35 + 11x + 6x2) = (3x + 1)(2x + -3) + 4x

Reorder the terms:
-35 + 11x + 6x2 = (1 + 3x)(2x + -3) + 4x

Reorder the terms:
-35 + 11x + 6x2 = (1 + 3x)(-3 + 2x) + 4x

Multiply (1 + 3x) * (-3 + 2x)
-35 + 11x + 6x2 = (1(-3 + 2x) + 3x * (-3 + 2x)) + 4x
-35 + 11x + 6x2 = ((-3 * 1 + 2x * 1) + 3x * (-3 + 2x)) + 4x
-35 + 11x + 6x2 = ((-3 + 2x) + 3x * (-3 + 2x)) + 4x
-35 + 11x + 6x2 = (-3 + 2x + (-3 * 3x + 2x * 3x)) + 4x
-35 + 11x + 6x2 = (-3 + 2x + (-9x + 6x2)) + 4x

Combine like terms: 2x + -9x = -7x
-35 + 11x + 6x2 = (-3 + -7x + 6x2) + 4x

Reorder the terms:
-35 + 11x + 6x2 = -3 + -7x + 4x + 6x2

Combine like terms: -7x + 4x = -3x
-35 + 11x + 6x2 = -3 + -3x + 6x2

Add '-6x2' to each side of the equation.
-35 + 11x + 6x2 + -6x2 = -3 + -3x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-35 + 11x + 0 = -3 + -3x + 6x2 + -6x2
-35 + 11x = -3 + -3x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-35 + 11x = -3 + -3x + 0
-35 + 11x = -3 + -3x

Solving
-35 + 11x = -3 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-35 + 11x + 3x = -3 + -3x + 3x

Combine like terms: 11x + 3x = 14x
-35 + 14x = -3 + -3x + 3x

Combine like terms: -3x + 3x = 0
-35 + 14x = -3 + 0
-35 + 14x = -3

Add '35' to each side of the equation.
-35 + 35 + 14x = -3 + 35

Combine like terms: -35 + 35 = 0
0 + 14x = -3 + 35
14x = -3 + 35

Combine like terms: -3 + 35 = 32
14x = 32

Divide each side by '14'.
x = 2.285714286

Simplifying
x = 2.285714286

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