4x^2+11x=7x+80

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Solution for 4x^2+11x=7x+80 equation: 


Simplifying
4x2 + 11x = 7x + 80

Reorder the terms:
11x + 4x2 = 7x + 80

Reorder the terms:
11x + 4x2 = 80 + 7x

Solving
11x + 4x2 = 80 + 7x

Solving for variable 'x'.

Reorder the terms:
-80 + 11x + -7x + 4x2 = 80 + 7x + -80 + -7x

Combine like terms: 11x + -7x = 4x
-80 + 4x + 4x2 = 80 + 7x + -80 + -7x

Reorder the terms:
-80 + 4x + 4x2 = 80 + -80 + 7x + -7x

Combine like terms: 80 + -80 = 0
-80 + 4x + 4x2 = 0 + 7x + -7x
-80 + 4x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-80 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + x + x2) = 0

Factor a trinomial.
4((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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