4x^2-3x=2x^2+7x

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


Simplifying
4x2 + -3x = 2x2 + 7x

Reorder the terms:
-3x + 4x2 = 2x2 + 7x

Reorder the terms:
-3x + 4x2 = 7x + 2x2

Solving
-3x + 4x2 = 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3x + -7x + 4x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: -3x + -7x = -10x
-10x + 4x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-10x + 2x2 = 7x + 2x2 + -7x + -2x2

Reorder the terms:
-10x + 2x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-10x + 2x2 = 0 + 2x2 + -2x2
-10x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5

Solution

x = {0, 5}

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