3x(x-2)=7x^2-7x

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


Simplifying
3x(x + -2) = 7x2 + -7x

Reorder the terms:
3x(-2 + x) = 7x2 + -7x
(-2 * 3x + x * 3x) = 7x2 + -7x
(-6x + 3x2) = 7x2 + -7x

Reorder the terms:
-6x + 3x2 = -7x + 7x2

Solving
-6x + 3x2 = -7x + 7x2

Solving for variable 'x'.

Reorder the terms:
-6x + 7x + 3x2 + -7x2 = -7x + 7x2 + 7x + -7x2

Combine like terms: -6x + 7x = 1x
1x + 3x2 + -7x2 = -7x + 7x2 + 7x + -7x2

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

Reorder the terms:
1x + -4x2 = -7x + 7x + 7x2 + -7x2

Combine like terms: -7x + 7x = 0
1x + -4x2 = 0 + 7x2 + -7x2
1x + -4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1x + -4x2 = 0

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