=x^2(4x+1)

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Solution for =x^2(4x+1) equation:


Simplifying
0 = x2(4x + 1)

Reorder the terms:
0 = x2(1 + 4x)
0 = (1 * x2 + 4x * x2)
0 = (1x2 + 4x3)

Solving
0 = 1x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-1x2 + -4x3 = 1x2 + 4x3 + -1x2 + -4x3

Reorder the terms:
-1x2 + -4x3 = 1x2 + -1x2 + 4x3 + -4x3

Combine like terms: 1x2 + -1x2 = 0
-1x2 + -4x3 = 0 + 4x3 + -4x3
-1x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-1x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(1 + 4x) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Solution

x = {0, -0.25}

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