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

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


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

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

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

Multiply (-7 + 4x) * (4 + 7x)
(-7(4 + 7x) + 4x * (4 + 7x)) = 0
((4 * -7 + 7x * -7) + 4x * (4 + 7x)) = 0
((-28 + -49x) + 4x * (4 + 7x)) = 0
(-28 + -49x + (4 * 4x + 7x * 4x)) = 0
(-28 + -49x + (16x + 28x2)) = 0

Combine like terms: -49x + 16x = -33x
(-28 + -33x + 28x2) = 0

Solving
-28 + -33x + 28x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

Solving
-4 + -7x = 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 + -7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7x = 0 + 4
-7x = 0 + 4

Combine like terms: 0 + 4 = 4
-7x = 4

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-0.5714285714, 1.75}

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