7x=4x^2+3

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


Simplifying
7x = 4x2 + 3

Reorder the terms:
7x = 3 + 4x2

Solving
7x = 3 + 4x2

Solving for variable 'x'.

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

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

Combine like terms: 3 + -3 = 0
-3 + 7x + -4x2 = 0 + 4x2 + -4x2
-3 + 7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + 7x + -4x2 = 0

Factor a trinomial.
(-1 + x)(3 + -4x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Solution

x = {1, 0.75}

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