3x^2+4x=x(-7x+8)

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Solution for 3x^2+4x=x(-7x+8) equation: 


Simplifying
3x2 + 4x = x(-7x + 8)

Reorder the terms:
4x + 3x2 = x(-7x + 8)

Reorder the terms:
4x + 3x2 = x(8 + -7x)
4x + 3x2 = (8 * x + -7x * x)
4x + 3x2 = (8x + -7x2)

Solving
4x + 3x2 = 8x + -7x2

Solving for variable 'x'.

Reorder the terms:
4x + -8x + 3x2 + 7x2 = 8x + -7x2 + -8x + 7x2

Combine like terms: 4x + -8x = -4x
-4x + 3x2 + 7x2 = 8x + -7x2 + -8x + 7x2

Combine like terms: 3x2 + 7x2 = 10x2
-4x + 10x2 = 8x + -7x2 + -8x + 7x2

Reorder the terms:
-4x + 10x2 = 8x + -8x + -7x2 + 7x2

Combine like terms: 8x + -8x = 0
-4x + 10x2 = 0 + -7x2 + 7x2
-4x + 10x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + 5x) = 0

Ignore the factor 2.

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 '(-2 + 5x)' equal to zero and attempt to solve:

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Divide each side by '5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0, 0.4}

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