(7x+8)(3x-4)=0

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Solution for (7x+8)(3x-4)=0 equation: 


Simplifying
(7x + 8)(3x + -4) = 0

Reorder the terms:
(8 + 7x)(3x + -4) = 0

Reorder the terms:
(8 + 7x)(-4 + 3x) = 0

Multiply (8 + 7x) * (-4 + 3x)
(8(-4 + 3x) + 7x * (-4 + 3x)) = 0
((-4 * 8 + 3x * 8) + 7x * (-4 + 3x)) = 0
((-32 + 24x) + 7x * (-4 + 3x)) = 0
(-32 + 24x + (-4 * 7x + 3x * 7x)) = 0
(-32 + 24x + (-28x + 21x2)) = 0

Combine like terms: 24x + -28x = -4x
(-32 + -4x + 21x2) = 0

Solving
-32 + -4x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1.142857143, 1.333333333}

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