(6x+7)(x-7)=(5x+5)(x-8)

Solution for (6x+7)(x-7)=(5x+5)(x-8) equation:

Simplifying
(6x + 7)(x + -7) = (5x + 5)(x + -8)

Reorder the terms:
(7 + 6x)(x + -7) = (5x + 5)(x + -8)

Reorder the terms:
(7 + 6x)(-7 + x) = (5x + 5)(x + -8)

Multiply (7 + 6x) * (-7 + x)
(7(-7 + x) + 6x * (-7 + x)) = (5x + 5)(x + -8)
((-7 * 7 + x * 7) + 6x * (-7 + x)) = (5x + 5)(x + -8)
((-49 + 7x) + 6x * (-7 + x)) = (5x + 5)(x + -8)
(-49 + 7x + (-7 * 6x + x * 6x)) = (5x + 5)(x + -8)
(-49 + 7x + (-42x + 6x2)) = (5x + 5)(x + -8)

Combine like terms: 7x + -42x = -35x
(-49 + -35x + 6x2) = (5x + 5)(x + -8)

Reorder the terms:
-49 + -35x + 6x2 = (5 + 5x)(x + -8)

Reorder the terms:
-49 + -35x + 6x2 = (5 + 5x)(-8 + x)

Multiply (5 + 5x) * (-8 + x)
-49 + -35x + 6x2 = (5(-8 + x) + 5x * (-8 + x))
-49 + -35x + 6x2 = ((-8 * 5 + x * 5) + 5x * (-8 + x))
-49 + -35x + 6x2 = ((-40 + 5x) + 5x * (-8 + x))
-49 + -35x + 6x2 = (-40 + 5x + (-8 * 5x + x * 5x))
-49 + -35x + 6x2 = (-40 + 5x + (-40x + 5x2))

Combine like terms: 5x + -40x = -35x
-49 + -35x + 6x2 = (-40 + -35x + 5x2)

Add '35x' to each side of the equation.
-49 + -35x + 35x + 6x2 = -40 + -35x + 35x + 5x2

Combine like terms: -35x + 35x = 0
-49 + 0 + 6x2 = -40 + -35x + 35x + 5x2
-49 + 6x2 = -40 + -35x + 35x + 5x2

Combine like terms: -35x + 35x = 0
-49 + 6x2 = -40 + 0 + 5x2
-49 + 6x2 = -40 + 5x2

Solving
-49 + 6x2 = -40 + 5x2

Solving for variable 'x'.

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

Add '-5x2' to each side of the equation.
-49 + 6x2 + -5x2 = -40 + 5x2 + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
-49 + 1x2 = -40 + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-49 + 1x2 = -40 + 0
-49 + 1x2 = -40

Add '49' to each side of the equation.
-49 + 49 + 1x2 = -40 + 49

Combine like terms: -49 + 49 = 0
0 + 1x2 = -40 + 49
1x2 = -40 + 49

Combine like terms: -40 + 49 = 9
1x2 = 9

Divide each side by '1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}