(2x+3)(6x-7)=(3x+5)(4x-3)

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Solution for (2x+3)(6x-7)=(3x+5)(4x-3) equation: 


Simplifying
(2x + 3)(6x + -7) = (3x + 5)(4x + -3)

Reorder the terms:
(3 + 2x)(6x + -7) = (3x + 5)(4x + -3)

Reorder the terms:
(3 + 2x)(-7 + 6x) = (3x + 5)(4x + -3)

Multiply (3 + 2x) * (-7 + 6x)
(3(-7 + 6x) + 2x * (-7 + 6x)) = (3x + 5)(4x + -3)
((-7 * 3 + 6x * 3) + 2x * (-7 + 6x)) = (3x + 5)(4x + -3)
((-21 + 18x) + 2x * (-7 + 6x)) = (3x + 5)(4x + -3)
(-21 + 18x + (-7 * 2x + 6x * 2x)) = (3x + 5)(4x + -3)
(-21 + 18x + (-14x + 12x2)) = (3x + 5)(4x + -3)

Combine like terms: 18x + -14x = 4x
(-21 + 4x + 12x2) = (3x + 5)(4x + -3)

Reorder the terms:
-21 + 4x + 12x2 = (5 + 3x)(4x + -3)

Reorder the terms:
-21 + 4x + 12x2 = (5 + 3x)(-3 + 4x)

Multiply (5 + 3x) * (-3 + 4x)
-21 + 4x + 12x2 = (5(-3 + 4x) + 3x * (-3 + 4x))
-21 + 4x + 12x2 = ((-3 * 5 + 4x * 5) + 3x * (-3 + 4x))
-21 + 4x + 12x2 = ((-15 + 20x) + 3x * (-3 + 4x))
-21 + 4x + 12x2 = (-15 + 20x + (-3 * 3x + 4x * 3x))
-21 + 4x + 12x2 = (-15 + 20x + (-9x + 12x2))

Combine like terms: 20x + -9x = 11x
-21 + 4x + 12x2 = (-15 + 11x + 12x2)

Add '-12x2' to each side of the equation.
-21 + 4x + 12x2 + -12x2 = -15 + 11x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-21 + 4x + 0 = -15 + 11x + 12x2 + -12x2
-21 + 4x = -15 + 11x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-21 + 4x = -15 + 11x + 0
-21 + 4x = -15 + 11x

Solving
-21 + 4x = -15 + 11x

Solving for variable 'x'.

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

Add '-11x' to each side of the equation.
-21 + 4x + -11x = -15 + 11x + -11x

Combine like terms: 4x + -11x = -7x
-21 + -7x = -15 + 11x + -11x

Combine like terms: 11x + -11x = 0
-21 + -7x = -15 + 0
-21 + -7x = -15

Add '21' to each side of the equation.
-21 + 21 + -7x = -15 + 21

Combine like terms: -21 + 21 = 0
0 + -7x = -15 + 21
-7x = -15 + 21

Combine like terms: -15 + 21 = 6
-7x = 6

Divide each side by '-7'.
x = -0.8571428571

Simplifying
x = -0.8571428571

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