2-(4x+1)(2-x)=x^2

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


Simplifying
2 + -1(4x + 1)(2 + -1x) = x2

Reorder the terms:
2 + -1(1 + 4x)(2 + -1x) = x2

Multiply (1 + 4x) * (2 + -1x)
2 + -1(1(2 + -1x) + 4x * (2 + -1x)) = x2
2 + -1((2 * 1 + -1x * 1) + 4x * (2 + -1x)) = x2
2 + -1((2 + -1x) + 4x * (2 + -1x)) = x2
2 + -1(2 + -1x + (2 * 4x + -1x * 4x)) = x2
2 + -1(2 + -1x + (8x + -4x2)) = x2

Combine like terms: -1x + 8x = 7x
2 + -1(2 + 7x + -4x2) = x2
2 + (2 * -1 + 7x * -1 + -4x2 * -1) = x2
2 + (-2 + -7x + 4x2) = x2

Combine like terms: 2 + -2 = 0
0 + -7x + 4x2 = x2
-7x + 4x2 = x2

Solving
-7x + 4x2 = x2

Solving for variable 'x'.

Combine like terms: 4x2 + -1x2 = 3x2
-7x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 3x) = 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 '(-7 + 3x)' equal to zero and attempt to solve: Simplifying -7 + 3x = 0 Solving -7 + 3x = 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 + 3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 0 + 7 3x = 0 + 7 Combine like terms: 0 + 7 = 7 3x = 7 Divide each side by '3'. x = 2.333333333 Simplifying x = 2.333333333

Solution

x = {0, 2.333333333}

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