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

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

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

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

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

Multiply (6 + x) * (-5 + 4x)
(6(-5 + 4x) + x(-5 + 4x)) = (3x + -2)(x + 7)
((-5 * 6 + 4x * 6) + x(-5 + 4x)) = (3x + -2)(x + 7)
((-30 + 24x) + x(-5 + 4x)) = (3x + -2)(x + 7)
(-30 + 24x + (-5 * x + 4x * x)) = (3x + -2)(x + 7)
(-30 + 24x + (-5x + 4x2)) = (3x + -2)(x + 7)

Combine like terms: 24x + -5x = 19x
(-30 + 19x + 4x2) = (3x + -2)(x + 7)

Reorder the terms:
-30 + 19x + 4x2 = (-2 + 3x)(x + 7)

Reorder the terms:
-30 + 19x + 4x2 = (-2 + 3x)(7 + x)

Multiply (-2 + 3x) * (7 + x)
-30 + 19x + 4x2 = (-2(7 + x) + 3x * (7 + x))
-30 + 19x + 4x2 = ((7 * -2 + x * -2) + 3x * (7 + x))
-30 + 19x + 4x2 = ((-14 + -2x) + 3x * (7 + x))
-30 + 19x + 4x2 = (-14 + -2x + (7 * 3x + x * 3x))
-30 + 19x + 4x2 = (-14 + -2x + (21x + 3x2))

Combine like terms: -2x + 21x = 19x
-30 + 19x + 4x2 = (-14 + 19x + 3x2)

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

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

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

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

Solving for variable 'x'.

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

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

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

Combine like terms: 3x2 + -3x2 = 0
-30 + 1x2 = -14 + 0
-30 + 1x2 = -14

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

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

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

Divide each side by '1'.
x2 = 16

Simplifying
x2 = 16

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