5x^2-6x+4=4x^2-4x+3

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Solution for 5x^2-6x+4=4x^2-4x+3 equation:


Simplifying
5x2 + -6x + 4 = 4x2 + -4x + 3

Reorder the terms:
4 + -6x + 5x2 = 4x2 + -4x + 3

Reorder the terms:
4 + -6x + 5x2 = 3 + -4x + 4x2

Solving
4 + -6x + 5x2 = 3 + -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
4 + -3 + -6x + 4x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2

Combine like terms: 4 + -3 = 1
1 + -6x + 4x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2

Combine like terms: -6x + 4x = -2x
1 + -2x + 5x2 + -4x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
1 + -2x + 1x2 = 3 + -4x + 4x2 + -3 + 4x + -4x2

Reorder the terms:
1 + -2x + 1x2 = 3 + -3 + -4x + 4x + 4x2 + -4x2

Combine like terms: 3 + -3 = 0
1 + -2x + 1x2 = 0 + -4x + 4x + 4x2 + -4x2
1 + -2x + 1x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
1 + -2x + 1x2 = 0 + 4x2 + -4x2
1 + -2x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
1 + -2x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {1, 1}

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