-x(9x+40)=x(-2x+3)

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Solution for -x(9x+40)=x(-2x+3) equation: 


Simplifying
-1x(9x + 40) = x(-2x + 3)

Reorder the terms:
-1x(40 + 9x) = x(-2x + 3)
(40 * -1x + 9x * -1x) = x(-2x + 3)
(-40x + -9x2) = x(-2x + 3)

Reorder the terms:
-40x + -9x2 = x(3 + -2x)
-40x + -9x2 = (3 * x + -2x * x)
-40x + -9x2 = (3x + -2x2)

Solving
-40x + -9x2 = 3x + -2x2

Solving for variable 'x'.

Reorder the terms:
-40x + -3x + -9x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: -40x + -3x = -43x
-43x + -9x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: -9x2 + 2x2 = -7x2
-43x + -7x2 = 3x + -2x2 + -3x + 2x2

Reorder the terms:
-43x + -7x2 = 3x + -3x + -2x2 + 2x2

Combine like terms: 3x + -3x = 0
-43x + -7x2 = 0 + -2x2 + 2x2
-43x + -7x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-43x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(43 + 7x) = 0

Ignore the factor -1.

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 '(43 + 7x)' equal to zero and attempt to solve:

Simplifying
43 + 7x = 0

Solving
43 + 7x = 0

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

Add '-43' to each side of the equation.
43 + -43 + 7x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 7x = 0 + -43
7x = 0 + -43

Combine like terms: 0 + -43 = -43
7x = -43

Divide each side by '7'.
x = -6.142857143

Simplifying
x = -6.142857143
Solution
x = {0, -6.142857143}

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