(4x+3)(x-7)=8x+6

Solution for (4x+3)(x-7)=8x+6 equation:

Simplifying
(4x + 3)(x + -7) = 8x + 6

Reorder the terms:
(3 + 4x)(x + -7) = 8x + 6

Reorder the terms:
(3 + 4x)(-7 + x) = 8x + 6

Multiply (3 + 4x) * (-7 + x)
(3(-7 + x) + 4x * (-7 + x)) = 8x + 6
((-7 * 3 + x * 3) + 4x * (-7 + x)) = 8x + 6
((-21 + 3x) + 4x * (-7 + x)) = 8x + 6
(-21 + 3x + (-7 * 4x + x * 4x)) = 8x + 6
(-21 + 3x + (-28x + 4x2)) = 8x + 6

Combine like terms: 3x + -28x = -25x
(-21 + -25x + 4x2) = 8x + 6

Reorder the terms:
-21 + -25x + 4x2 = 6 + 8x

Solving
-21 + -25x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
-21 + -6 + -25x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -21 + -6 = -27
-27 + -25x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -25x + -8x = -33x
-27 + -33x + 4x2 = 6 + 8x + -6 + -8x

Reorder the terms:
-27 + -33x + 4x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
-27 + -33x + 4x2 = 0 + 8x + -8x
-27 + -33x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-27 + -33x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.75, 9}