7x(x-2)=3-2(x+4)

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


Simplifying
7x(x + -2) = 3 + -2(x + 4)

Reorder the terms:
7x(-2 + x) = 3 + -2(x + 4)
(-2 * 7x + x * 7x) = 3 + -2(x + 4)
(-14x + 7x2) = 3 + -2(x + 4)

Reorder the terms:
-14x + 7x2 = 3 + -2(4 + x)
-14x + 7x2 = 3 + (4 * -2 + x * -2)
-14x + 7x2 = 3 + (-8 + -2x)

Combine like terms: 3 + -8 = -5
-14x + 7x2 = -5 + -2x

Solving
-14x + 7x2 = -5 + -2x

Solving for variable 'x'.

Reorder the terms:
5 + -14x + 2x + 7x2 = -5 + -2x + 5 + 2x

Combine like terms: -14x + 2x = -12x
5 + -12x + 7x2 = -5 + -2x + 5 + 2x

Reorder the terms:
5 + -12x + 7x2 = -5 + 5 + -2x + 2x

Combine like terms: -5 + 5 = 0
5 + -12x + 7x2 = 0 + -2x + 2x
5 + -12x + 7x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
5 + -12x + 7x2 = 0

Factor a trinomial.
(5 + -7x)(1 + -1x) = 0

Subproblem 1

Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143

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 = {0.7142857143, 1}

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