(5x+4z)x(2x-7z)=

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


Simplifying
(5x + 4z) * x(2x + -7z) = 0

Reorder the terms for easier multiplication:
x(5x + 4z)(2x + -7z) = 0

Multiply (5x + 4z) * (2x + -7z)
x(5x * (2x + -7z) + 4z * (2x + -7z)) = 0
x((2x * 5x + -7z * 5x) + 4z * (2x + -7z)) = 0

Reorder the terms:
x((-35xz + 10x2) + 4z * (2x + -7z)) = 0
x((-35xz + 10x2) + 4z * (2x + -7z)) = 0
x(-35xz + 10x2 + (2x * 4z + -7z * 4z)) = 0
x(-35xz + 10x2 + (8xz + -28z2)) = 0

Reorder the terms:
x(-35xz + 8xz + 10x2 + -28z2) = 0

Combine like terms: -35xz + 8xz = -27xz
x(-27xz + 10x2 + -28z2) = 0
(-27xz * x + 10x2 * x + -28z2 * x) = 0

Reorder the terms:
(-28xz2 + -27x2z + 10x3) = 0
(-28xz2 + -27x2z + 10x3) = 0

Solving
-28xz2 + -27x2z + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-28z2 + -27xz + 10x2) = 0

Factor a trinomial.
x((-4z + -5x)(7z + -2x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-4z + -5x)' equal to zero and attempt to solve:

Simplifying
-4z + -5x = 0

Reorder the terms:
-5x + -4z = 0

Solving
-5x + -4z = 0

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

Add '4z' to each side of the equation.
-5x + -4z + 4z = 0 + 4z

Combine like terms: -4z + 4z = 0
-5x + 0 = 0 + 4z
-5x = 0 + 4z
Remove the zero:
-5x = 4z

Divide each side by '-5'.
x = -0.8z

Simplifying
x = -0.8z

Subproblem 3
Set the factor '(7z + -2x)' equal to zero and attempt to solve:

Simplifying
7z + -2x = 0

Reorder the terms:
-2x + 7z = 0

Solving
-2x + 7z = 0

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

Add '-7z' to each side of the equation.
-2x + 7z + -7z = 0 + -7z

Combine like terms: 7z + -7z = 0
-2x + 0 = 0 + -7z
-2x = 0 + -7z
Remove the zero:
-2x = -7z

Divide each side by '-2'.
x = 3.5z

Simplifying
x = 3.5z
Solution
x = {0, -0.8z, 3.5z}

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