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

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


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

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

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

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

Combine like terms: -21x + 2x = -19x
(-14 + -19x + 3x2) = (x + -6)(4x + 5)

Reorder the terms:
-14 + -19x + 3x2 = (-6 + x)(4x + 5)

Reorder the terms:
-14 + -19x + 3x2 = (-6 + x)(5 + 4x)

Multiply (-6 + x) * (5 + 4x)
-14 + -19x + 3x2 = (-6(5 + 4x) + x(5 + 4x))
-14 + -19x + 3x2 = ((5 * -6 + 4x * -6) + x(5 + 4x))
-14 + -19x + 3x2 = ((-30 + -24x) + x(5 + 4x))
-14 + -19x + 3x2 = (-30 + -24x + (5 * x + 4x * x))
-14 + -19x + 3x2 = (-30 + -24x + (5x + 4x2))

Combine like terms: -24x + 5x = -19x
-14 + -19x + 3x2 = (-30 + -19x + 4x2)

Add '19x' to each side of the equation.
-14 + -19x + 19x + 3x2 = -30 + -19x + 19x + 4x2

Combine like terms: -19x + 19x = 0
-14 + 0 + 3x2 = -30 + -19x + 19x + 4x2
-14 + 3x2 = -30 + -19x + 19x + 4x2

Combine like terms: -19x + 19x = 0
-14 + 3x2 = -30 + 0 + 4x2
-14 + 3x2 = -30 + 4x2

Solving
-14 + 3x2 = -30 + 4x2

Solving for variable 'x'.

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

Add '-4x2' to each side of the equation.
-14 + 3x2 + -4x2 = -30 + 4x2 + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
-14 + -1x2 = -30 + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-14 + -1x2 = -30 + 0
-14 + -1x2 = -30

Add '14' to each side of the equation.
-14 + 14 + -1x2 = -30 + 14

Combine like terms: -14 + 14 = 0
0 + -1x2 = -30 + 14
-1x2 = -30 + 14

Combine like terms: -30 + 14 = -16
-1x2 = -16

Divide each side by '-1'.
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}

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